On pathological properties of fixed point algebras in Kirchberg algebras

We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group Gamma and any infinite group Lambda, we construct an outer action of Lambda on the Cuntz algebra O-2 whose fixed point algebra is almost equal to the reduced group C*-algebra C-r(*)(Gamma). Moreover, we show that every infinite group admits outer actions on all Kirchberg algebras whose fixed point algebras fail the completely bounded approximation property.