Dovermann–Suh conjecture on inducing Smith exotic actions

Let $G$ be an Oliver group and let $N$ be a normal subgroup such that

$$\operatorname{Ind}_N^G:\operatorname{RO}(N)\rightarrow\operatorname{RO}(G)$$

is a monomorphism. A finite group is an Oliver group if it satisfies the Oliver condition, and a Smith exotic action is an action with the relevant Smith fixed-point data that is not equivalent to a linear action. Dovermann–Suh conjecture. If $N$ admits Smith exotic actions, then $G$ admits Smith exotic actions as well. This is a proposed induction principle for Smith exotic actions. The conjecture is refuted: counterexamples are given in Pawalowski (2018).