  A Q-system in a C* 2-category is a unitary version of a separable Frobenius
algebra object and can be viewed as a unitary version of a higher idempotent.
We define a higher unitary idempotent completion for C* 2-categories called
Q-system completion and study its properties. We show that the C* 2-category of
right correspondences of unital C*-algebras is Q-system complete by
constructing an inverse realization $\dag$ 2-functor. We use this result to
construct induced actions of group theoretical unitary fusion categories on
continuous trace C*-algebras with connected spectra.
