Kono–Yagita even-degree conjecture for Brown–Peterson cohomology

Let $G$ be a compact Lie group and let $BG$ be its classifying space. Kono–Yagita's even-degree conjecture. The Brown–Peterson cohomology $BP^*(BG)$ is concentrated in even degrees. This conjecture is presented as closely related to Totaro's conjecture and concerns the grading of Brown–Peterson cohomology for classifying spaces. The supplied text gives no resolution, so it remains open here.