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