  In this article we study cohomology of a group with coefficients in
representations on Banach spaces and its stability under deformations. We show
that small, metric deformations of the representation preserve vanishing of
cohomology. As applications we obtain deformation theorems for fixed point
properties on Banach spaces. In particular, our results yield fixed point
theorems for affine actions in which the linear part is not uniformly bounded.
Our proofs are effective and allow for quantitative estimates.
