Bialgebra cyclic homology with coefficients

We show that one can extend the definition of Hopf cyclic homology with coefficients such that one can use bialgebras and a larger class of coefficient module/co-modules. With the help of this extension, we calculate the bialgebra cyclic homology of U _q (g) the quantum deformation of an arbitrary semi-simple Lie algebra and g and H(N) the Hopf algebra of foliations of codimension N, with several coefficient modules.