2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75989The main goal of this paper is to give the first examples of equivariant aspherical Poincare complexes, that are not realized by group actions on closed aspherical manifolds $M$. These will also provide new counterexamples to the Nielsen realization problem about lifting homotopy actions of finite groups to honest group actions. Our examples show that one cannot guarantee that a given action of a finitely generated group $π$ on Euclidean space extends to an action of $Π$, a group containing $π$ as a subgroup of finite index, even when all the torsion of $Π$ lives in $π$.Geometric Topology57Ntext