Geometric fixed points of norms for finite subgroups with trivial adjoint action

Let $G$ be a compact Lie group, let $K<G$ be finite, and let $X$ be an input for the norm $N_e^G$. Assume that the adjoint action of $K$ on $T_eG$ is trivial, so that $K\backslash G$ inherits a parallelization from $G$. Finite-subgroup geometric fixed-point conjecture. For the composite of derived functors $\Phi^K N_e^G$, there is a natural weak equivalence in the non-equivariant stable category

$$(N_e^G X)^{\Phi K}\simeq \int_{K\backslash G}X.$$

This gives the expected factorization-homology description of geometric fixed points. When $K$ is normal, the right-hand side is identifiable with $N_e^{G/K}X$, and the source further conjectures a refinement to a weak equivalence of genuine $G/K$-spectra.