  By studying the group of self homotopy equivalences of the localization (at a
prime $p$ and/or zero) of some aspherical complexes, we show that, contrary to
the case when the considered space is a nilpotent complex, $\mathcal{E}_{\#}^m
(X_{p})$ is in general different from $\mathcal{E}_{\#}^m (X)_{p}$. That is the
case even when $X=K(G,1)$ is a finite complex and/or $G$ satisfies extra
finiteness or nilpotency conditions, for instance, when $G$ is finite or
virtually nilpotent.
