  In this paper, we compute the cyclic homology of the Taft algebras and of
their Auslander algebras. Given a Hopf algebra $\Lambda,$ the Grothendieck
groups of projective $\Lambda -$modules and of all $\Lambda -$modules are
endowed with a ring structure, which in the case of the Taft algebras is
commutative (\cite{C2}, \cite{G}). We also describe the first Chern character
for these algebras.
