  We introduce a K-theoretic invariant for actions of unitary fusion categories
on unital C*-algebras. We show that for inductive limits of finite dimensional
actions of fusion categories on unital AF-algebras, this is a complete
invariant. In particular, this gives a complete invariant for inductive limit
actions of finite groups on AF-algebras. We apply our results to obtain a
classification of finite depth, strongly AF-inclusions of unital AF-algebras.
