Let G be a semisimple Lie group with finite component group, and let K<G
be a maximal compact subgroup. We obtain a quantisation commutes with reduction
result for actions by G on manifolds of the form M=GΓKβN, where N
is a compact prequantisable Hamiltonian K-manifold. The symplectic form on
N induces a closed two-form on M, which may be degenerate. We therefore
work with presymplectic manifolds, where we take a presymplectic form to be a
closed two-form. For complex semisimple groups and semisimple groups with
discrete series, the main result reduces to results with a more direct
representation theoretic interpretation. The result for the discrete series is
a generalised version of an earlier result by the author. In addition, the
generators of the K-theory of the Cβ-algebra of a semisimple group are
realised as quantisations of fibre bundles over suitable coadjoint orbits