  We study (pre-)sheaves in bicategories on geometric categories: smooth
manifolds, manifolds with a Lie group action and Lie groupoids. We present
three main results: we describe equivariant descent, we generalize the plus
construction to our setting and show that the plus construction yields a
2-stackification for 2-prestacks. Finally we show that, for a 2-stack, the
pullback functor along a Morita-equivalence of Lie groupoids is an equivalence
of bicategories. Our results have direct applications to gerbes and 2-vector
bundles. For instance, they allow to construct equivariant gerbes from local
data and can be used to simplify the description of the local data. We
illustrate the usefulness of our results in a systematic discussion of
holonomies for unoriented surfaces.
