Adams's detection conjecture for mod-$p$ cohomology of compact Lie groups

Let $G$ be a compact connected Lie group, let $p$ be an odd prime, and let $\mathcal{E}_p(G)$ represent the conjugacy classes of maximal elementary abelian $p$-subgroups of $G$. Consider the restriction map

$$\Phi:H^*(BG;\mathbb{F}_p)\to\prod_{E\in\mathcal{E}_p(G)}H^*(BE;\mathbb{F}_p).$$

Adams's detection conjecture. For every compact connected Lie group $G$ and every odd prime $p$, the map $\Phi$ is injective. This strengthens Quillen's result that the kernel contains only nilpotent elements. The paper's abstract states that the conjecture has counterexamples for suitable projective unitary groups, so the claim is refuted.