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We construct dense, unconditional subalgebras of the reduced group$C^*$-algebra of a word-hyperbolic group, which are closed under holomorphicfunctional calculus and possess many bounded traces. Applications to the cycliccohomology of group $C^*$-algebras and to delocalized $L^2$-invariants ofnegatively curved manifolds are given.

New holomorphically closed subalgebras of $C^*$-algebras of hyperbolic groups