  Let $\Gamma$ be a finitely generated group of matrices over $\mathbb{C}$. We
construct an isometric action of $\Gamma$ on a complete CAT(0) space $X$ such
that the restriction of this action to any subgroup of $\Gamma$ containing no
nontrivial unipotent elements is well behaved. As an application, we show that
if $M$ is a graph manifold that does not admit a nonpositively curved
Riemannian metric, then any finite-dimensional $\mathbb{C}$-linear
representation of $\pi_1(M)$ maps a nontrivial element of $\pi_1(M)$ to a
unipotent matrix. In particular, the fundamental groups of such 3-manifolds do
not admit any faithful finite-dimensional unitary representations.
