  It is shown that the breakdown of a {\it global} symmetry group to a discrete
subgroup can lead to analogues of the Aharonov-Bohm effect. At sufficiently low
momentum, the cross-section for scattering of a particle with nontrivial $\Z_2$
charge off a global vortex is almost equal to (but definitely different from)
maximal Aharonov-Bohm scattering; the effect goes away at large momentum. The
scattering of a spin-1/2 particle off a magnetic vortex provides an amusing
experimentally realizable example.
