Let $X$ be an abelian variety over a field $k$. Let $G$ be a finite group scheme over $k$ acting on $X$ and denote $X/G$ to be the geometric quotient of $X$ by $G$, which always exists in this case. My question is this:
Is $X/G$ an abelian variety over $k$?
I understand that it is a group scheme of finite type over $k$.