  Beilinson's resolution of the diagonal for complex projective space was
generalized by Bayer-Popescu-Sturmfels for any unimodular toric variety. Here,
we give a resolution of the diagonal for any smooth toric variety (viewed as a
toric Deligne-Mumford stack) in families by deformation of the cellular complex
of Bayer-Popescu-Sturmfels and show that the cokernel of this resolution gives
the diagonal, modulo torsion from the irrelevant ideal. Furthermore, we give a
resolution of the diagonal for a toric Deligne-Mumford stack associated to the
global quotient of a smooth toric variety by a finite abelian group.

Algebraic Geometry;K-Theory and Homology