On the nonexistence of higher twistings over a point for Borel cohomology of KK-theory

In this note we show that there are no higher twistings for the Borel cohomology theory associated to GG-equivariant KK-theory over a point and for a compact Lie group GG. Therefore, twistings over a point for this theory are classified by the group H1(BG,Z/2)×H3(BG,Z)H1(BG,Z/2)×H3(BG,Z).