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fixed point algebras

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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On pathological properties of fixed point algebras in Kirchberg algebras
Part of
- Selfadjoint operator algebras
- Locally compact groups and their algebras
Yuhei Suzuki
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 6 / December 2020

Published online by Cambridge University Press:

20 September 2019, pp. 3087-3096

Print publication:

December 2020
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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.