Functorial cyclic-homology decomposition for quotient schemes

Let $X$ be a quasiprojective scheme over a field $k$, let $G$ be a finite group acting on $X$, and assume that $\operatorname{char} k$ does not divide $|G|$. Let $\operatorname{Coh}(X)$ be the exact category of coherent sheaves on $X$, and let $\operatorname{Coh}_G(X)$ be the exact category of $G$-equivariant sheaves. For each $g\in G$, write $X^g$ for the fixed-point subscheme. The cyclic-homology decomposition conjecture. For every $W$ of finite projective dimension over $k[u]$, there exists an isomorphism

$$\phi_X:\left(\bigoplus_{g\in G}HC_\bullet(\operatorname{Coh}(X^g),W)\right)_G\longrightarrow HC_\bullet(\operatorname{Coh}_G(X),W)$$

that is functorial with respect to derived pushforwards under $G$-equivariant proper maps. This conjecture is motivated by the corresponding decomposition for smooth varieties and by the relation between equivariant cyclic homology and orbifold cohomology. The source gives no resolution status.