The Bloch-type motive decomposition conjecture for finite quotients

Let $X$ be a smooth projective variety over a field $k$ of characteristic $0$, and let $G$ be a finite group acting on $X$. Suppose that

$$H^i(X,\mathcal{O}_{X})=H^i(X,\mathcal{O}_{X})^G$$

for all $i$. Write $(X,\pi)$ for the motive associated with the quotient map $\pi:X\to X/G$, and let $Y$ be a resolution of singularities of $X/G$. Then there exist effective motives $N$ and $N'$ such that

$$X\cong (X,\pi)\oplus N'\otimes\mathbb{Q}(-1),\qquad Y\cong (X,\pi)\oplus N\otimes\mathbb{Q}(-1).$$

This is the motive decomposition predicted by the Bloch conjectures for zero-cycles on finite quotients; the supplied text does not indicate whether it has been proved or disproved in this generality.