Poly-ℤ Group Actions on Kirchberg Algebras I

Abstract

Abstract Toward the complete classification of poly-${\mathbb{Z}}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an application of them, we classify outer actions of poly-${\mathbb{Z}}$ groups of Hirsch length not greater than three on unital Kirchberg algebras up to $KK$-trivial cocycle conjugacy.