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O’Dwyer faces extradition to the US and up to 10 years in prison for creating a website, TVShack.net, which linked to places to watch TV and movies online.
O'Dwyer, who was still a teenager when he set up the TVShack.net website, is accused of breaching copyright by posting links to pirated film and television content.
Even though he has never been to the US or used web servers in US territory, he is wanted by authorities there because most of the content featured on his site was made in the US.
In March, home secretary Theresa May approved the extradition of the computer science student to the US to face trial for copyright breach.
Wales’ petition calls on the home secretary to stop the extradition on the grounds that “O'Dwyer is not a US citizen, he's lived in the UK all his life, his site was not hosted there, and most of his users were not from the US”.
Battle between content industry and internet users
Writing in the Guardian, Jimmy Wales said: "When I met Richard, he struck me as a clean-cut, geeky kid. Still a university student, he is precisely the kind of person we can imagine launching the next big thing on the internet.
"Given the thin case against him, it is an outrage that he is being extradited to the US to face felony charges for something that he is not being prosecuted for here. No US citizen has ever been brought to the UK for alleged criminal activity that took place on US soil.
"From the beginning of the internet, we have seen a struggle between the interests of the "content industry" and the interests of the general public. Due to heavy lobbying and much money lavished on politicians, until very recently the content industry has won every battle.
"We, the users of the internet, handed them their first major defeat earlier this year with the epic Sopa/Pipa protests which culminated in a widespread internet blackout and 10 million people contacting the US Congress to voice their opposition.
"Together, we won the battle against Sopa and Pipa. Together, we can win this one too," said Wales.
Signing the petition, O’Dwyer's mother Julia said: “This is not only a matter of British national importance, but of global importance too. We so appreciate Jimmy Wales launching this petition in support of Richard. To have such support and endorsement from such a knowledgeable and respected figure is fantastic. I hope many will follow Jimmy's lead.”
Legal intricacies of content sharing
O'Dwyer remains in the UK pending an appeal to the high court, to be heard later this year. His defence team argues that his alleged conduct was not an offence under UK law. His website did not host pirated material itself, but acted as a directory of links.
A UK attempt in 2010 to prosecute the operators of a similar website, TV-Links, failed because of European laws that protect firms against copyright infringement claims if they have little influence over the material to which they link.
O'Dwyer's defence said his site had the same protection, but the judge in his extradition hearing ruled that, because he was involved in deciding who was allowed to post links on the website, his alleged conduct was a criminal offence under UK copyright law.
Other US extraditions, such as those of alleged computer hacker Gary McKinnon, have led to calls for reform of the US/UK extradition treaty, which campaigners say is biased against UK interests.
McKinnon, an Asperger Syndrome sufferer, is still fighting extradition to the US to face charges of hacking into US military computers in 2002.