  For a unitary representation of the fundamental group of a compact smooth
manifold, Atiyah, Patodi, Singer defined the so called alpha-invariant of the
representation using Chern-Simons invariants. In this article using traces on
C*-algebras, we define intrinsically(i.e without using Chern character) an
element in KK-theory with real coefficients theory whose pullback by the
representation is the alpha-invariant.
