  We consider group-valued cocycles over a partially hyperbolic diffeomorphism
which is accessible volume-preserving and center bunched. We study cocycles
with values in the group of invertible continuous linear operators on a Banach
space. We describe properties of holonomies for fiber bunched cocycles and
establish their Holder regularity. We also study cohomology of cocycles and its
connection with holonomies. We obtain a result on regularity of a measurable
conjugacy, as well as a necessary and sufficient condition for existence of a
contionuous conjugacy between two cocycles.
