Trace Invariant and Cyclic Cohomology of Twisted Group C*-Algebras

By the method of cyclic cohomology we prove that all tracial states on a twisted group C *( G ;σ), where G is a torsion free discrete group of polynomial growth and σ is a 2-cocycle on G with values in the unit circle group, induce the same map from K 0 ( C *( G ;σ)) into R .