Let $X$ an affine normal scheme of finite type over a field $k$ of characteristic zero. Let $G$ a finite group acting on $X$ and $Y=X/G=Spec(K[X]^{G})$.

We assume that $Y=\mathbb{A}^{n}=k[f_{1},\dots,f_{n}]$ with $f_{i}\in K[X]^{G}$.

Then we have a finite flat surjective morphism $\pi:X\rightarrow Y$ generically étale of group $G$.

Do we have that $\pi$ is a complete intersection?