  In the first part of this series, we defined an equivariant index without
assuming the group acting or the orbit space of the action to be compact. This
allowed us to generalise an index of deformed Dirac operators, defined for
compact groups by Braverman. In this paper, we investigate properties and
applications of this index. We prove that it has an induction property that can
be used to deduce various other properties of the index. In the case of compact
orbit spaces, we show how it is related to the analytic assembly map from the
Baum-Connes conjecture, and an index used by Mathai and Zhang. We use the index
to define a notion of K-homological Dirac induction, and show that, under
conditions, it satisfies the quantisation commutes with reduction principle.
