Every Kirchberg algebra admits rigid, KK-equivalent, maximal embeddings into non-nuclear and non-exact simple C*-algebras, via perturbed free group crossed products.
Poly-$\mathbb{Z}$ group actions on Kirchberg algebras I
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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.
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Non-amenable tight squeezes by Kirchberg algebras
Every Kirchberg algebra admits rigid, KK-equivalent, maximal embeddings into non-nuclear and non-exact simple C*-algebras, via perturbed free group crossed products.