  We study D-branes on smooth noncompact toric Calabi-Yau manifolds that are
resolutions of abelian orbifold singularities. Such a space has a distinguished
basis {S_i} for the compactly supported K-theory. Using local mirror symmetry
we demonstrate that the S_i have simple transformation properties under
monodromy; in particular, they are the objects that generate monodromy around
the principal component of the discriminant locus. One of our examples, the
toric resolution of C^3/(Z_2 x Z_2), is a three parameter model for which we
are able to give an explicit solution of the GKZ system.
