Kono–Yagita nilpotence conjecture for Brown–Peterson cohomology

Let $G$ be a compact Lie group, let $BG$ be its classifying space, and let $BP^*(BG)$ denote its Brown–Peterson cohomology ring. Kono–Yagita's nilpotence conjecture. The ring $BP^*(BG)$ has no nonzero nilpotent elements. The paper explains that its proposed examples would give counterexamples to this conjecture, but the supplied text does not establish that the relevant elements are nilpotent in $BP^*(BPU(n))$. Its status therefore remains open from the supplied evidence.