Minimal orbifolds and (a)symmetry of piecewise locally symmetric manifolds

We show that if $g$ is a Riemannian metric on a closed piecewise locally symmetric manifold $M$, then the lift of $g$ to the universal cover $\tilde{M}$ has a discrete isometry group. We also show that the index $[\text{Isom}(\tilde{M}):{\pi }_1(M)]$ is bounded by a constant independent of $g$.