Let $V/G$ be the orbit space of a finite group $G$ of automorphisms of a complex projective variety $V$. Is $V/G$ a projective variety?

Example: $V/G$ is the space of sets in complex projective $n$-space $P$, of cardinality $\le k$. Here $V=P\times\dots\times P$ ($k$ factors) and $G$ is the permutation group on $k$ letters.