Authors’ summary: Let \(G\) be a word hyperbolic group in the sense of Gromov and \(P\) its associated Rips complex. We prove that the fixed point set \(P^H\) is contractible for every finite subgroup \(H\) of \(G\). This is the main ingredient for proving that \(P\) is a finite model for the universal space \(\underline EG\) for proper actions. As a corollary we get that a hyperbolic group has only finitely many conjugacy classes of finite subgroups.