Ruan's cohomological crepant resolution conjecture

Let $M$ be a smooth projective variety endowed with a faithful action of a finite group $G$, and let $X:=M/G$ be its quotient. Assume that $X$ is Gorenstein, and let $Y\to X$ be any crepant resolution. More generally, let $\mathcal X$ be a smooth proper orbifold with underlying singular variety $X$ Gorenstein, and let $Y\to X$ be any crepant resolution. Ruan's cohomological crepant resolution conjecture. There is an isomorphism of graded $\mathbf C$-algebras

$$H^{*}_{qc}(Y,\mathbf C)\simeq H^{*}_{orb}([M/G],\mathbf C),$$

and, in the more general orbifold setting,

$$H^{*}_{qc}(Y,\mathbf C)\simeq H^{*}_{orb}(\mathcal X,\mathbf C).$$

This conjecture proposes that the quantum-corrected cohomology of a crepant resolution agrees multiplicatively with the orbifold cohomology of the corresponding quotient or orbifold. The source notes that the isomorphism is known in several cases, including symplectic resolutions, but does not establish the full statement here.