  Based on the ideas of Cuntz and Quillen, we give a simple construction of
cyclic homology of unital algebras in terms of the noncommutative de Rham
complex and a certain differential similar to the equivariant de Rham
differential. We describe the Connes exact sequence in this setting.
  We define equivariant Deligne cohomology and construct, for each n > 0, a
natural map from cyclic homology of an algebra to the GL_n-equivariant Deligne
cohomology of the variety of n-dimensional representations of that algebra. The
bridge between cyclic homology and equivariant Deligne cohomology is provided
by extended cyclic homology, which we define and compute here, based on the
extended noncommutative de Rham complex introduced previously by the authors.
