  We introduce a slight modification of the usual equivariant $KK$-theory. We
use this to give a $KK$-theoretical proof of an equivariant index theorem for
Dirac-Schrodinger operators on a non-compact manifold of nowhere positive
curvature. We incidentally show that the boundary of Dirac is Dirac;
generalizing earlier work of Baum and coworkers, and a result of Higson and
Roe.
