  We present a geometric approach, in the spirit of the Chern-Weil theory, for
constructing cocycles representing the classes of the Hopf cyclic cohomology of
the Hopf algebra H(n) relative to GL(n, R). This provides an explicit
description of the universal Hopf cyclic Chern classes, which complements our
earlier geometric realization of the Hopf cyclic characteristic classes of
foliations.
