Nielsen realization for aspherical closed manifolds with hyperbolic fundamental group

Let $M$ be an aspherical closed manifold with hyperbolic fundamental group $\pi$. Let $j\colon G\to \operatorname{Out}(\pi)$ be an embedding of a finite group $G$ into the outer automorphism group of $\pi$. Let $\operatorname{Aut}(M)$ denote the group of self-homeomorphisms of $M$, and let $\nu\colon \operatorname{Aut}(M)\to \operatorname{Out}(\pi)$ be the canonical map induced by the action on the fundamental group. Nielsen realization conjecture. There is an effective topological $G$-action $\rho\colon G\to \operatorname{Aut}(M)$ on $M$ such that

$$\nu\circ\rho=j.$$

This asserts that every finite subgroup of the outer automorphism group of a hyperbolic fundamental group is realized by an effective topological action on the corresponding aspherical closed manifold. The source notes that, to the authors' knowledge, there is no counterexample; the general status is not established here.