  Motivated by classical facts concerning closed manifolds, we introduce a
strong finiteness property in K-homology. We say that a C*-algebra has
uniformly summable K-homology if all its K-homology classes can be represented
by Fredholm modules which are finitely summable over the same dense subalgebra,
and with the same degree of summability. We show that two types of C*-algebras
associated to hyperbolic groups - the C*-crossed product for the boundary
action, and the reduced group C*-algebra - have uniformly summable K-homology.
We provide explicit summability degrees, as well as explicit finitely summable
representatives for the K-homology classes.
