The motivic McKay correspondence for linear actions I

Let $\mathfrak{X}$ and $\mathfrak{V}$ be centered log structures on $X=V/G$ and $V$, respectively, and let $\mathfrak{V}^{|F|}$ be the induced centered log structure on $V^{|F|}$. Assume the morphisms in the associated diagram are crepant. Let $M_{\mathrm{st}}(\mathfrak{X})$ be the stringy motif and let

$$M_{\mathrm{st}}^{G}(\mathfrak{V})=\int_{J_\infty^G\mathfrak{V}}\mathbb{L}^{\mathbf{f}_{\mathfrak{V}}+\mathbf{w}_V}\,d\mu_{\mathfrak{V}}^G$$

be the orbifold stringy motif.

The motivic McKay correspondence for linear actions I. We have

$$M_{\mathrm{st}}(\mathfrak{X})=M_{\mathrm{st}}^{G}(\mathfrak{V}).$$

This is the linear-action motivic McKay correspondence, deduced in the paper from the conjectural linear change-of-variables formula. The source gives no resolution.