Every compact group arises as the outer automorphism group of a II1 factor

We show that any compact group can be realized as the outer automorphism group of a factor of type II1. This has been proved in the abelian case by Ioana, Peterson and Popa [A. Ioana, J. Peterson, S. Popa, Amalgamated free products of w-rigid factors and calculation of their symmetry group, math.OA/0505589, Acta Math., in press] applying Popa's deformation/rigidity techniques to amalgamated free product von Neumann algebras. Our methods are a generalization of theirs.