Quasi-Invariant States For Amenable Discrete Groups

We generalize results on quasi-invariant states from compact to discrete amenable group actions on unital C*-algebras. Assuming a faithful invariant tracial state, we use Folner averages to construct a conditional expectation onto the fixed-point algebra. When the second cohomology group [Formula: see text]) = 0, we show that every quasi-invariant state with full central support has a GNS representation unitarily equivalent to that of an invariant state obtained by averaging. This provides a complete discrete analogue of the compact case.