  We study D-branes and Ramond-Ramond fields on global orbifolds of Type II
string theory with vanishing H-flux using methods of equivariant K-theory and
K-homology. We illustrate how Bredon equivariant cohomology naturally realizes
stringy orbifold cohomology. We emphasize its role as the correct cohomological
tool which captures known features of the low-energy effective field theory,
and which provides new consistency conditions for fractional D-branes and
Ramond-Ramond fields on orbifolds. We use an equivariant Chern character from
equivariant K-theory to Bredon cohomology to define new Ramond-Ramond couplings
of D-branes which generalize previous examples. We propose a definition for
groups of differential characters associated to equivariant K-theory. We derive
a Dirac quantization rule for Ramond-Ramond fluxes, and study flat
Ramond-Ramond potentials on orbifolds.
