This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it.

Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite group $G$ is acting on $X$ and its quotient is an $S$-scheme $X//G$.

Is the quotient projective or at least proper? (I have seen versions of this over fields but not for arbitrary base.)