Is it possible for someone to remotely manipulate the keys on my computer to make it look like I was typing?
closed as too broad by Terry Chia, Iszi, Adnan, Rory Alsop♦ Oct 8 at 8:37
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Most desktop remote tools or in a more malicious method through a Remote Administration Tool normally allow the user to use both a mouse and keyboard for input.
To put it bluntly, yes someone could infect your computer and perform a web search which would appear to have been from your PC & IP.