Virus 'caught' while using Linux lays dormant, becomes active when login into Windows, can it be?

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http://unix.stackexchange.com – Can I 'catch' a Windows virus, while using Linux - so it will be saved on my hard drive and start working when I log in to Windows? I know it wouldn't affect the Linux itself. I am using 'Dual boot', not operating both systems at the same time. Also, would a harming change, caused by, say - a spyware, to my browser (Chrome), while surfing when using 'Linux' appear again when I open my 'Chrome' on Windows ? (HowTos)