Crepant birational invariance of stringy motifs

Let $\mathfrak{X}$ and $\mathfrak{X}'$ be centered log $D$-varieties, and let $f:\mathfrak{X}\to\mathfrak{X}'$ be a proper, birational and crepant morphism. Let $M_{\mathrm{st}}(\mathfrak{X})$ and $M_{\mathrm{st}}(\mathfrak{X}')$ denote their stringy motifs.

Crepant invariance conjecture. If $f$ is proper, birational and crepant, then

$$M_{\mathrm{st}}(\mathfrak{X})=M_{\mathrm{st}}(\mathfrak{X}').$$

This is the expected invariance of stringy motifs under crepant birational modifications and underlies the McKay formulas developed in the paper. The source presents it conjecturally and gives no general resolution.