  Let (M,\omega,\Phi) be a Hamiltonian T-space and let H be a closed Lie
subtorus of T. Under some technical hypotheses on the moment map \Phi, we prove
that there is no additive torsion in the integral full orbifold K-theory of the
orbifold symplectic quotient [M//H]. Our main technical tool is an extension to
the case of moment map level sets the well-known result that components of the
moment map of a Hamiltonian T-space M are Morse-Bott functions on M. As first
applications, we conclude that a large class of symplectic toric orbifolds, as
well as certain S^1-quotients of GKM spaces, have integral full orbifold
K-theory that is free of additive torsion. Finally, we introduce the notion of
semilocally Delzant which allows us to formulate sufficient conditions under
which the hypotheses of the main theorem hold. We illustrate our results using
low-rank coadjoint orbits of type A and B.
