# Examples of CAT(0)-groups

My question is the following:

Let M be a simply connected Riemannian manifold whose sectional curvatures are all nonpositive and let G be a group. Suppose that G acts in M properly discontinuous and cocompactly by isometries. Is G a CAT(0) group?

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The answer is yes, since $M$ is a $CAT(0)$ space, and the group is quasi-isometric to it. See (for example) Jim Cannon's article in Bedford Keane Series:
By definition, a group is $CAT(0)$ if it acts isometrically, properly and co-compactly on a $CAT(0)$ space... So it is enough to say that $M$ is $CAT(0)$. See aimath.org/pggt/… –  Alain Valette Dec 10 '11 at 18:33