Actions of tensor categories on Kirchberg algebras

We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unitary tensor categories on Kirchberg algebras. In particular, every countable unitary tensor category admits an outer action on the Cuntz algebra O₂. We also discuss the realizability of modules over fusion rings as K-groups of Kirchberg algebras acted by unitary tensor categories. Several new examples are provided, among which actions on Cuntz algebras of 3-cocycle twists of cyclic groups are constructed for all possible 3-cohomological classes by answering a question asked by Izumi.