  We study C*-algebra endomorphims which are special in a weaker sense w.r.t.
the notion introduced by Doplicher and Roberts. We assign to such endomorphisms
a geometrical invariant, representing a cohomological obstruction for them to
be special in the usual sense. Moreover, we construct the crossed product of a
C*-algebra by the action of the dual of a (nonabelian, noncompact) group of
vector bundle automorphisms. These crossed products supply a class of examples
for such generalized special endomorphisms.
