Let $G$ be a finite group acting on $\mathbb A^n_{\mathbb C}$. Let $Y$ be a dense open whose complemenent is of codimension at least two. 

Assume   $Y$ is $G$-stable, the action of $G$ is free on $Y$, and that $Y/G$ is a quasi-affine scheme.

Is the action of $G$ on $\mathbb A^n_{\mathbb C}$ free?