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.