i think that should be great to create a simple and open source pvr, because all the other pvr are really expensive.
I know that this can't be based on arduino beacuse it has a low speed serial communication but i think that in this forum there are a lot of people who can help me.
You want to look up MythTV (http://www.mythtv.org/, http://en.wikipedia.org/wiki/MythTV). MythTV is distributed under the GNU public license (GPL). It is available on most Linux distributions as pre-built executables, but if not, you should be able to configure and build it.
You will need a much bigger system than the Arduino, which doesn't have the memory nor processor speed to deal with high speed video. I would suggest browsing the MythTV site to find what is needed for your particular application.
In the US, it is now a requirement that the HD-TV signals be encrypted, and you would need some way to decrypt the video stream if you are getting signals from cable.