$L^p$-cohomology for groups of isometries of Hadamard spaces

We show that a discrete group $\mathrm{\Gamma }$ which admits a non-elementary isometric action on a Hadamard manifold of bounded negative curvature admits an isometric action on an $L^p$-space $V$ for some $p>1$ with $H^1(\mathrm{\Gamma },V)≠0$.