  We consider cocycles of isometries on spaces of nonpositive curvature $H$. We
show that the supremum of the drift over all invariant ergodic probability
measures equals the infimum of the displacements of continuous sections under
the cocycle dynamics. In particular, if a cocycle has uniform sublinear drift,
then there are almost invariant sections, that is, sections that move
arbitrarily little under the cocycle dynamics. If, in addition, $H$ is a
symmetric space, then we show that almost invariant sections can be made
invariant by perturbing the cocycle.
