Wave the Swallow/History and appearances

Early life
Wave was born into the Babylon clan of thieves known as the Babylon Rogues. She is a descendant of the Babylonians, an alien race that stranded on earth in ancient times and became a legendary band of thieves which continued their legacy of thieving for generations.

During her early life, Wave was raised and given her skills by her father. At some point, she became a member of the Babylon Rogues and was joined by Jet the Hawk and Storm the Albatross. Together, the three of them formed the newest generation of Babylon Rogues and continued their clan's legacy of theft, with Wave serving as the team's technological genius and Extreme Gear mechanic.

During her career as a member Babylon Rogues, Wave and her team engaged in a number of unknown criminal activities and managed to build up an infamous reputation.

Sonic Riders
In Sonic Riders, Wave and Storm found Dr. Eggman arriving on their airship with a proposition for Jet. When the two brought the news to Jet, she noticed Jet's Key to Babylon Garden, which could reveal Babylon Garden and its hidden treasure, but Storm kept her from it. Eggman then arrived and revealed the Key to Babylon Garden could reveal Babylon Garden if they collected the seven Chaos Emeralds, though he warned Sonic the Hedgehog would get in their way. Wanting their ancestors' treasure, the Babylon Rogues agreed to work with Eggman.

As their plan, the doctor hosted the EX World Grand Prix, where the contestants had to pay an entry free of one Chaos Emerald, and the winner got to claim all seven. Wave and her team then only had to win the competition. Traveling to Future City, Wave and her team stole a Chaos Emerald as an entry feed. While fleeing, Wave caught Storm when he was hit by Knuckles and got away.

After entering the EX World Grand Prix and passing the first rounds, Wave met Team Sonic so she could see their Extreme Gear. After checking Tails' Blue Star, Wave secretly planted a bomb on it, before dismissing it as a piece of junk and left. In the follow race, she beat Amy and advanced further in the competition.

Back at their headquarters, Wave began arguing with Storm of how he blamed her for losing to Knuckles, until Jet told them he suspected Eggman was hiding something and sent Storm to find what the doctor could be hiding. As Wave and Jet awaited Storm's return, Wave began to fret while lecturing Jet on his responsibilities, until she saw Jet had snuck away. Soon after, Wave lost to Tails in an official race and was eliminated from the World Grand Prix.

At the finals, Wave and Jet met Storm, having brought Eggman's diary with him. As Wave examined it, the group learned that the Treasure of Babylon was not a gem as Eggman made them believe, but actually the Babylonians' advanced technology, which the doctor hoped to use for world domination. When Jet then tried to leave, Wave convinced him to stay and win the finals by stating the possibility that the treasure could still be valuable. In the finals, Jet almost lost to Sonic, but Wave detonated the bomb on Sonic's Blue Star, allowing Jet to win. When Jet then unearth Babylon Garden with the Chaos Emeralds and the Key to Babylon Garden, Eggman stole the Key and went after the treasure himself, promoting Wave and the others to chase after him.

Arriving on Babylon Garden, Wave and Storm challenged Tails and Knuckles, but were forced to leave when E-10000s attacked. When they found Jet, Wave took the Key to Babylon Garden on Jet's behalf when he refused and entered Babylon Garden to get the treasure, but accidentally awoke the Babylon Guardian. With the arrival of Team Sonic and Amy, Wave and the others defeated the Babylon Guardian and found the Treasure of Babylon, which was a Magic Carpet, much to Eggman's disappointment. Wave and Tails however, saw that it was an ancient prototype of Extreme Gear. With the ordeal over, Wave and the rest of the Babylon Rogues left Sonic and his friends until next time.

Sonic Riders: Zero Gravity
In Sonic Riders: Zero Gravity, a few months after the World Grand Prix, Wave and her team were on a treasure hunt to Gigan Rocks to find an Ark of the Cosmos, an engine unit for Babylon Garden. After getting the Ark of the Cosmos, Wave tried to make a wish on a shooting star despite being ridiculed by Storm. However, some falling meteors created tremors that activated the ruins' trap, causing some boulders to drop down on them. However, Wave and her team were saved when Jet used the Ark of the Cosmos.

Back on the their airship, Wave began analyzing the Ark of the Cosmos and told Jet about her finds. Having also read some Babylonian scrolls that there were five Arks of the Cosmos, Wave was ready to build a radar to find them when Storm came with a news report saying that a SCR-GP stole an Ark of the Cosmos from the Megalo City Museum, promoting the team to head for Megalo Station.

Arriving in Monopole, Wave and Storm followed Jet and the robot with the Ark of the Cosmos to a dome, There, Wave saw Sonic, Knuckles, Tails, and Amy were there, and that they had the Ark of the Cosmos they were looking for. Overhearing the group planned to go to MeteorTech, Wave, Jet and Storm went ahead to gather information. Arriving at MeteorTech, Wave helped Jet repel the security robots with the Ark of the Cosmos and reunited with Sonic's group, with Wave greeting Tails. When more security robots showed up though, Sonic and his friends left, with Wave and Jet chasing after them.

When they got to the control room, Wave and the others found Dr. Eggman, who owned MeteorTech. Under persuasion, the doctor revealed that the MeteorTech mother computer had an Ark of the Cosmos, and that the robots that were currently on a global rampage were collecting more Arks of the Cosmos which was due to the Arks of the Cosmos' influence. Wave and the others then noticed that both Amy and Storm were gone and saw on monitor images that Storm and SCR-HD were chasing Amy.

Returning to the Babylon Rogues' airship, Wave worked on deciphering some ancient Babylonian texts until Storm returned with two Arks of the Cosmos. Wave told her team that she had discovered in the ancient texts that the Arks of the Cosmos were severed from Babylon Garden's engine because they almost triggered a "lightless black," something she had no idea about what was. No sooner though, Wave and the others discovered that two of their Arks of the Cosmos had been stolen by Eggman, who planned to use them to take control of the world's robots and conquer the world. Wasting no time, the Babylon Rogues followed Eggman.

Arriving at the Crimson Tower, Wave and her team met Sonic and his friends, and Wave explained to them about the Crimson Tower. She and her team then raced against Sonic and his friends to Eggman with the Arks of the Cosmos at stake.

At the end of the race, which ended with a tie, Eggman and the global robot rampage were stopped. When Babylon Garden appeared due to all Arks of the Cosmos being present and Sonic handed over his, Wave prepared to head to Babylon Garden with her team and the Arks of the Cosmos. However, she was attacked by SCR-HD, who stole all the Arks of the Cosmos from her and took them to Babylon Garden. This transformed Babylon Garden into Astral Babylon and created a black hole, the "lightless black", which would consume the planet. After figuring out a plan to stop the black hole, Wave and her team followed Team Sonic to Astral Babylon, where they faced and defeated Master Core: ABIS, saving the world. With everything over, Wave asked Jet if he was okay with the truth about their ancestry. Hearing that Jet was content with it, Wave took her leave with her team.

Sonic Free Riders
In Sonic Free Riders, Wave and the Babylon Rogues entered the newest World Grand Prix hosted by Dr. Eggman as Team Babylon to seek fame. When Omochao had an interview with the team, Wave was inpatient to get the cash prize, though she agreed with Jet that she should pity their first opponents.

In the first round, Team Babylon faced Team Dark, who Wave advised to ignore after they trash-talked them. Between the races, Wave tried to defend Jet when Rouge rebuked his complements and had to deal with Storm arguing with E-10000B which she thought was a pointless endeavor. After they beat Team Dark, Wave remained confident her team would win the Grand Prix.

In their next race, Team Babylon faced Team Rose. As Team Babylon won over their opponents again and again, Wave taunted Vector with how he had to deal with his annoying team-mates.

After defeating Team Rose, Team Babylon advanced to the finals with Team Heroes, though Wave was confident Team Heroes could not win with Tails's Extreme Gear. During the face-off, Wave secretly sabotaged Team Heroes' Extreme Gear with Storm. Before the final race against Team Heroes, Wave taunted Tails and assured Jet they would win, which made Jet suspicious that she had cheated, but Wave played innocent. After the race, Jet accused Wave for Team Heroes' mechanical issues during the race, but Wave denied it. Regardless, Jet ensured Team Babylon's victory in a rematch, and Wave praised Jet for his victory. As Team Babylon was hailed as winners, Wave taunted Tails about not expecting to match her in Extreme Gear expertise, but still encouraged him.

As the Grand Prix continued, Team Babylon lost a few times too, with Wave being confident before the race, only to be in disbelief (once even in denial) when beaten. After the tournament was over, Wave and the other teams went to the awards ceremony to collect their prizes but Eggman made all of the competitors race against his "ultimate Gear-jockey robot". After winning the race, Eggman revealed that he used the World Grand Prix to gather the riders' racing data with his E-10000 robots to create the ultimate Extreme Gear which he could use for his own agenda. Eggman then challenged Wave and the others to a race, but lost, and Wave mocked the doctor's inability to determine the problem, before dismissing Storm's suggestion to take the racing data, finding it useless. Metal Sonic then revealed himself as the one controlling E-10000B and passing fake data to Eggman, while taking the real data himself in an effort to beat Sonic on Extreme Gear.

Wave and the others then saw Sonic and Metal Sonic square off in a rival race to the finish, with Sonic winning. As the World Grand Prix came to a close and it was revealed the prizes were fake, Wave was upset about leaving the competition empty-handed since it would kill the Babylon Rogues' reputation.

Super Smash Bros. Brawl
In Super Smash Bros. Brawl, Wave appears as a collectible Sticker:

Mario & Sonic at the London 2012 Olympic Games
In Mario & Sonic at the London 2012 Olympic Games, Wave does not appear in person. However, she makes a cameo appearance in the form of a costume for the Mii.

Mario & Sonic at the Rio 2016 Olympic Games
In Mario & Sonic at the Rio 2016 Olympic Games, Wave appears as a playable character.