  A duality is discussed for Lie group bundles vs. certain tensor categories
with non-simple identity, in the setting of Nistor-Troitsky gauge-equivariant
K-theory. As an application, we study C*-algebra bundles with fibre a
fixed-point algebra of the Cuntz algebra: a classification is given, and a
cohomological invariant is assigned, representing the obstruction to perform an
embedding into a continuous bundle of Cuntz algebras. Finally, we introduce the
notion of twisted equivariant K-theory.
