May's equivariant complex K-theory comparison conjecture

Let $G$ be a compact Lie group, let $MU_G$ denote $G$-equivariant complex cobordism, and let $KU_G$ denote equivariant complex K-theory. The relative smash product $MU_G\wedge_{MU}KU$ is an $MU_G$-module spectrum. May's equivariant complex K-theory comparison conjecture. The spectrum

$$MU_G\wedge_{MU}KU$$

is equivalent to $KU_G$ in the category of $MU_G$-module spectra for $G$ a compact Lie group. The paper's subsequent discussion states that this conjecture of May is false for all nontrivial compact Lie groups, so the conjecture is refuted in that range.