The multiplicative cohomology conjecture for Burnside Tambara functors

Let $G$ be a finite group, and let $\underline{A}_G$ be the Burnside $G$-Tambara functor.

Multiplicative Burnside conjecture.

$$\underline{A}^{\mathrm{mult}}=\underline{\mathbb{Z}}.$$

The result is proved for nilpotent finite groups, and the statement for all finite groups is left open.