Poly-$${\mathbb {Z}}$$ group actions on Kirchberg algebras II

Abstract

This is the second part of our serial work on the classification of poly- $${\mathbb {Z}}$$ group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer $${\mathbb {Z}}^n$$ -actions on the Cuntz algebras.