Suppose $X$ is smooth proper algebraic $\mathbb C$-variety with algebraic action of a finite abelian group $G$. Suppose I know that

- $X/G$ (good geometric quotient) exists and it is normal Gorenstein Calabi-Yau variety (Calabi-Yau means here that dualizing sheaf is trivial).
- There is exactly one $\mathbb C$-point $p \in X$ such that stabilizer $G_p \subset G$ is non-trivial ($\neq \{e\}$). Moreover, $G_p = G$, so $p$ is a fixed point.
- Crepant resolution of $(T_p X)/G_p$ exists.

Can I deduce that crepant resolution of $X/G$ also exists?

The reason why I am asking is that in an analytical setting the question of crepant resolutions of general Calabi-Yau manifolds could be reduced to the question of crepant resolutions of $\mathbb C^n/G$. For example, in Crepant Resolutions of Calabi-Yau Orbifolds author says

A Calabi-Yau manifold is a complex Kahler manifold with trivial canonical bundle. ... An orbifold is the quotient of a smooth Calabi-Yau manifold by a discrete group action that generically has fixed points. Locally such an orbifold is modeled on $\mathbb C^n/G$... A resolution $(X, \pi)$ of $\mathbb C^n/G$ is a nonsingular complex manifold X of dimension n with a proper biholomorphic map $\pi : X → \mathbb C^n/G$ that induces a biholomorphism between dense open sets.

Сan something similar take place in the algebraic setting as well?