Wireless spying

Is it possible to view my web history from a computer if I am a member of a wireless network with that computer? The network just allows me to use the internet and I do that through a router. The coputer that the router is hooked up to is not able to view any of my files or anything as it is set up just for an internet connection. I am new to this whole hacking thing an I would prefer if no one found out I was doing it.

Unless you root the box, no.

Thank you for the answer.