Finitely summable $\gamma$-elements for word-hyperbolic groups

We present two explicit combinatorial constructions of finitely summable reduced “Gamma”-elements $\gamma\_r\in KK(C^\*\_r(\Gamma),\mathbb{C})$ for any word-hyperbolic group $(\Gamma,S)$ and obtain summability bounds them in terms the cardinality generating set $S\subset\Gamma$ hyperbolicity constant associated Cayley graph.