New, out-of-state, registration fees??

Please help!

I wanted to buy a "new" vehicle from a dealer out of state because I
won't have to pay sales tax. But I was told that I would have to pay
the tax once I register the vehicle in my home state (CA - California).
Does anyone know if this is true or if there is a way to get around
having to pay the full taxes?

I know when you buy used, a lot of people just write the purchase price
really low. But how does the DMV check on these things?

Thanks!