Totaro's Chow–Brown–Peterson comparison conjecture

Let $G$ be a complex linear algebraic group, let $p$ be a prime, and suppose that $BP^*(BG)$ is concentrated in even degrees. For each $i$, consider the localized cycle map

$$CH^i(BG)_{(p)}\to BP^{2i}(BG)\otimes_{BP^*}\mathbb{Z}_{(p)}.$$

Totaro's conjecture. Under these hypotheses, this map is an isomorphism. The conjecture compares the Chow ring with Brown–Peterson cohomology after localization. No resolution is supplied in the given text, so it remains open here.