Does Google Scan My PC?

Hello, I'm wondering if anyone knows whether logging in to your Google account, for "Groups" and "Gmail", etc., gives Google permission to scan your PC.
I've noticed that, on several occasions, my computer will slow down; or the "My Computer" directory will, suddenly, open by itself.
Sometimes, when I type into a textbox, the text appears slowly.
All this usually happens when I log in to my Google account.
Any help or opinions will be appreciated.
(If I posted this in the wrong forum, please let me know.)

 

I dont use Groups but I log on to Gmail (three accounts) several times per day and have not noticed any slowdown or hard drive activity. Atleast Gmail should not do anything with your computer. If that happend to me I would do a hijackthis and an online antivirus scan.