  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 $\mathcal{O}_2$. 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.
