On the classification of group actions on C*-algebras up to equivariant KK-equivalence

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. show that any action is equivariantly KK-equivalent an a simple, purely infinite C*-algebra. conjecture Izumi equivalent equivalence between cocycle conjugacy and KK-equivalence for torsion-free amenable groups Kirchberg algebras. Let G be cyclic prime order. describe its KK-equivalence, based previous work by Manuel K\"ohler. In particular, we classify stabilised Cuntz algebras in bootstrap class