Nonnegative Curvature, Symmetry and Fundamental Group

We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two splitting in a finite cover theorems for isometric group actions on Riemannian manifolds with infinite fundamental groups, where the manifolds are either compact of Ric 0, or complete of sec 0. The result is used to construct Lie group actions that are isometric in some metric of scal > 0 and that are not isometric in any metric of Ric 0.