Let $k$ be a field. Let $X$ be a scheme over $k.$ Let $G$ be an affine smooth group scheme over $k$ acting on $X.$ Suppose $X$ is of finite type over $k.$ Does this guarantee that the quotient stack $[X/G]$ is of finite type?
We know $[X/G]$ is locally of finite type over $k$. So the question is whether $[X/G]$ is quasi-compact.