  We show that superselection structures on curved spacetimes, that are
expected to describe quantum charges affected by the underlying geometry, are
categories of sections of presheaves of symmetric tensor categories. When an
embedding functor is given, the superselection structure is a Tannaka-type dual
of a locally constant group bundle, which hence becomes a natural candidate for
the role of gauge group. Indeed, we show that any locally constant group bundle
(with suitable structure group) acts on a net of C*-algebras fulfilling normal
commutation relations on an arbitrary spacetime. We also give examples of
gerbes of C*-algebras, defined by Wightman fields and constructed using
projective representations of the fundamental group of the spacetime, that we
propose as solutions for the problem that existence and uniqueness of the
embedding functor are not guaranteed.
