  A base $\Delta$ generating the topology of a space $M$ becomes a partially
ordered set (poset), when ordered under inclusion of open subsets. Given a
precosheaf over $\Delta$ of fixed-point spaces (typically C*-algebras) under
the action of a group $G$, in general one cannot find a precosheaf of
$G$-spaces having it as fixed-point precosheaf. Rather one gets a gerbe over
$\Delta$, that is, a "twisted precosheaf" whose twisting is encoded by a
cocycle with coefficients in a suitable 2-group. We give a notion of holonomy
for a gerbe, in terms of a non-abelian cocycle over the fundamental group
$\pi_1(M)$. At the C*-algebraic level, holonomy leads to a general notion of
twisted C*-dynamical system, based on a generic 2-group instead of the usual
adjoint action on the underlying C*-algebra. As an application of these
notions, we study presheaves of group duals (DR-presheaves) and prove that the
dual object of a DR-presheaf is a group gerbe over $\Delta$. It is also shown
that any section of a DR-presheaf defines a twisted action of $\pi_1(M)$ on a
Cuntz algebra.
