Strong Novikov conjecture for low degree cohomology and exotic group $C$*-algebras

We strengthen a result of Hanke-Schick about the strong Novikov conjecture for low degree cohomology by showing that their non-vanishing result for the maximal group C*-algebra holds for many other exotic group C*-algebras, in particular the one associated to the smallest strongly Morita compatible and exact crossed product functor used in the new version of the Baum-Connes conjecture. To achieve this we provide a Fell absorption principle for certain exotic crossed product functors.