  By deploying dense subalgebras of $\ell^1(G)$ we generalize the Bass
conjecture in terms of Connes' cyclic homology theory. In particular, we
propose a stronger version of the $\ell^1$-Bass Conjecture. We prove that
hyperbolic groups relative to finitely many subgroups, each of which posses the
polynomial conjugacy-bound property and nilpotent periodicity property, satisfy
the $\ell^1$-Stronger-Bass Conjecture. Moreover, we determine the
conjugacy-bound for relatively hyperbolic groups and compute the cyclic
cohomology of the $\ell^1$-algebra of any discrete group.
