  We consider reduced crossed products of twisted C*-dynamical systems over
C*-simple groups. We prove there is a bijective correspondence between maximal
ideals of the reduced crossed product and maximal invariant ideals of the
underlying C*-algebra, and a bijective correspondence between tracial states on
the reduced crossed product and invariant tracial states on the underlying
C*-algebra. In particular, the reduced crossed product is simple if and only if
the underlying C*-algebra has no proper non-trivial invariant ideals, and the
reduced crossed product has a unique tracial state if and only if the
underlying C*-algebra has a unique invariant tracial state. We also show that
the reduced crossed product satisfies an averaging property analogous to
Powers' averaging property.
