The equivariant multiplicative McKay conjecture

Let $V$ be a symplectic vector space, let $G$ act symplectically on $V$, and let $X\to V/G$ be a symplectic resolution. The natural dilation action of $\mathbb C^*$ on $V$ lifts to $X$, and $u$ denotes the degree-two generator of $H^*(B\mathbb C^*)=\mathbb C[u]$. If $F_i(\mathsf ZG)$ is the filtration on the center of the group algebra and

$$\operatorname{Rees}_\bullet(\mathsf ZG)=\sum_i F_i(\mathsf ZG)u^i\subset \mathsf ZG[u],$$

then the equivariant multiplicative McKay conjecture. There is a canonical graded $\mathbb C[u]$-algebra isomorphism

$$H^\bullet_{\mathbb C^*}(X,\mathbb C)\cong \operatorname{Rees}_\bullet(\mathsf ZG).$$

This is an equivariant refinement of the multiplicative McKay correspondence; the source states that the corresponding nonequivariant algebra isomorphism is proved, but gives no resolution status for this equivariant formulation.