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On pathological properties of fixed point algebras in Kirchberg algebras

  • Yuhei Suzuki (a1)


We investigate how the fixed point algebra of a C*-dynamical system can differ from the underlying C*-algebra. For any exact group Γ and any infinite group Λ, we construct an outer action of Λ on the Cuntz algebra 𝒪2 whose fixed point algebra is almost equal to the reduced group C*-algebra ${\rm C}_{\rm r}^* (\Gamma)$ . Moreover, we show that every infinite group admits outer actions on all Kirchberg algebras whose fixed point algebras fail the completely bounded approximation property.



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On pathological properties of fixed point algebras in Kirchberg algebras

  • Yuhei Suzuki (a1)


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