Let a finite group $G\subset SL(n,\mathbb{C})$ act on $\mathbb{C}^{n}$ in a natural way. Assume there is a crepant resolution of $f:X\rightarrow \mathbb{C}^{n}/G$. When is it possible to write $X$ as $Y/G$ for some $Y$ and $G$-action on $Y$?

This is true for example $\pm id_{\mathbb{C}^{2}} \subset SL(2,\mathbb{C})$ acting on $\mathbb{C}^{2}$. Is it still true for example $$ \langle diag(e^{\frac{2\pi i}{3}},e^{\frac{2\pi i}{3}},e^{\frac{2\pi i}{3}})\rangle \cong \mathbb{Z}/3\mathbb{Z} \subset SL(n,\mathbb{C}) $$ acting on $\mathbb{C}^{3}$? FYI, this has toric crepant resolution.