People are interested in the cohomology rings for various reasons. One of the properties they look at is whether the cohomology ring of an object is finitely generated. In this talk, we show that some skew group algebras have Noetherian cohomology rings, a property inherited from their component parts. The proof is an adaptation of Evens' proof of finite generation of group cohomology. We apply the result to a series of examples of finite dimensional Hopf algebras in positive characteristic. This is joint work with S. Witherspoon.