  We apply the classical technique on cyclic objects of Alain Connes to various
objects, in particular to the higher Chow complex of S. Bloch to prove a Connes
periodicity long exact sequence involving motivic cohomology groups. The Cyclic
higher Chow groups and the Connes higher Chow groups of a variety are defined
in the process and various properties of them are deduced from the known
properties of the higher Chow groups. Applications include an equivalent
reformulation of the Beilinson-Soul\'e vanishing conjecture for the motivic
cohomology groups of a smooth variety $X$ and a reformulation of the conjecture
of Soul\'e on the order of vanishing of the zeta function of an arithmetic
variety.
