# reference request – Cohomology of quotient by free action

Let $$G$$ be a finite group. Let $$G$$ act freely on a CW-complex $$X$$. I heard that the following fact is true.

Claim. The canonical map $$H^*(X/G,F)to H^*(X,F)^G$$ is an isomorphism, where $$F$$ is a field so that $$|G|$$ is invertible.

I am looking for a reference to this fact.