  Starting from a collection of line bundles on a projective toric orbifold X,
we introduce a stacky analogue of the classical linear series. Our first main
result extends work of King by building moduli stacks of refined
representations of labelled quivers. We associate one such stack to any
collection of line bundles on X to obtain our notion of a stacky linear series;
as in the classical case, X maps to the ambient stack by evaluating sections of
line bundles in the collection. As a further application, we describe a finite
sequence of GIT wall crossings between [A^n/G] and G-Hilb(A^n) for a finite
abelian subgroup G of SL(n,k) where n is less than or equal to 3.
