McKay correspondence conjecture for crepant resolutions

Let $G\subset \operatorname{Sl}_n(\mathbb C)$ be a finite group, put $W=\mathbb C^n/G$, and let $X\rightarrow W$ be a crepant resolution. Write $D^b_G(\mathbb C^n)$ for the bounded derived category of $G$-equivariant coherent sheaves on $\mathbb C^n$. McKay correspondence conjecture. The categories $D^b(X)$ and $D^b_G(\mathbb C^n)$ should be derived equivalent.

$$D^b(X)\simeq D^b_G(\mathbb C^n).$$

This is a non-commutative analogue of the crepant-resolution conjecture, relating a crepant resolution to the quotient stack or equivariant geometry of the singular quotient. The source presents the statement as a conjecture and gives no resolution status.