Mr McKinnon, who has Asperger's syndrome, is accused of hacking US military computer systems in 2002.
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Mr McKinnon accessed 97 government computers belonging to organisations including the US Navy and Nasa.
Mr McKinnon, who hacked into the US computers in 2002, has been fighting extradition since 2006.
Glasgow-born Mr McKinnon, 43, who has Asperger's syndrome, is accused of breaking into US military computers.
Mr McKinnon's mother says her son "had no choice" but to refuse fresh medical tests.
Mrs May announces that she has decided to block Mr McKinnon's extradition to the United States.
In one case, McKinnon allegedly crashed computers belonging to the Military District of Washington.
McKinnon has previously said it was easy for him to access the secret files.
"I did occasionally leave messages in system administrators' machines saying, 'This is ridiculous, '" McKinnon has said.
In August 2008 Mr McKinnon was diagnosed with Asperger's syndrome - a form of autism.
McKinnon admitted being concerned in the supply of heroin at his home in May 2011.
The Chair of the New Zealand National Commission for UNESCO, Ian McKinnon said the achievement was to be celebrated.
But how did Mr McKinnon's fight become such a rallying cause for this disparate group of supporters?
Were he to be tried and convicted, McKinnon could have faced 60 years in a U.S. prison.
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Home Secretary Alan Johnson told Mr McKinnon's family he could not block the move on medical grounds.
Mr McKinnon admits hacking into 97 US government computers, including Nasa's and Pentagon's, during 2001 and 2002.
Mr McKinnon, 46, admits accessing US government computers but claims he was looking for evidence of UFOs.
In Scotland, McKinnon arranged for the drugs to be sold on from his home in Niddrie, Edinburgh.
"Somehow they found out where the kids were, " said Detective Larry McKinnon of the Hillsborough County sheriff's office.
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Todd McKinnon is CEO and Co-founder of Okta, a cloud application management service set to launch in January.
Glasgow-born Gary McKinnon could face life in jail if convicted of accessing 97 US military and Nasa computers.
Rena Liu (left) and Amiee Zang receive National Commission for UNESCO Award from Ian McKinnon, Chairman, New Zealand Commission for UNESCO.
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His MP, David Burrowes, who had threatened to resign as a parliamentary aide if Mr McKinnon was extradited, welcomed the decision.
If there is no UK prosecution, Mr McKinnon would inevitably be extradited to stand trial in the US, the judges heard.
Lozano has said she was returning a pair of pants to The Gap for her boss, Mark McKinnon.
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Mr McKinnon's lawyer Karen Todner said she had "mixed feelings" about the decision.
It is now up to British prosecutors to decide if McKinnon should face charges in the United Kingdom.
FORBES: Hacker Gary McKinnon Avoids Extradition To United States
Mr McKinnon's lawyers and family have fought a series of long-running court battles in an attempt to avoid extradition.
The computer systems Mr McKinnon, now of Wood Green, north London, is accused of breaking into include the Pentagon.
It now looked as though the US would try to prosecute Mr McKinnon as a cyber-terrorist, Mr Anderson said.
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