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On 12 September 2000, Google announced the addition of Simplified and Traditional Chinese versions to Google.com and began to provide search services for Chinese users worldwide.
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On 2 September 2002, BBC News reported that access to Google was blocked in China before China's change of leadership in November (http://news.bbc.co.uk/2/hi/technology/2231101.stm). The blockake lasted for two weeks.
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On 19 July 2005, Kai-Fu Lee (李开复), a former Microsoft executive and the founder in 1998 of Microsoft Research Asia, joined Google and officially became the president of Google in China.
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Google.cn, a censorship compliant search engine or 谷歌中国 formally launched
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In March 2009 China blocked access to Google's YouTube site due to footage showing Chinese security forces beating Tibetans. (https://www.nytimes.com/2009/03/25/technology/internet/25youtube.html)
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On 4 September 2009, after four years leading Google China, Kai-Fu Lee unexpectedly left Google amid debate about the Chinese government's censorship policies
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In January 2010 Google announced that, in response to a Chinese-originated hacking attack on them and other US tech companies, they were no longer willing to censor searches in China and would pull out of the country completely if necessary.
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Google formally exited China market, removed its google.cn service and transferred all requests to its hong kong site.
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Google Transparency Report shows that Google was completely blocked in China since June 2014. Technically speaking, Google cannot detect any search requests to any Google services from IPs residing in China.
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News about Google returning to China never stopped. The most well-known episode is certainly the Dragonfly project unexpectedly disclosed by Google employees.