Suppose you have a separated Deligne Mumford quotient stack $[V/G]$ over a field of characteristic $0$, where $V$ is a quasiprojective variety and $G$ is an algebraic group that does **not** necessarily act linearly on $V$.

What can we say about the coarse moduli space? What are necessary and sufficient conditions for the coarse moduli space to be a quasiprojective scheme? Same question for a proper Deligne Mumford stack of the same form.