Abstract: There is a result from the 1980's that allows us to describe the equivariant $K$-theory of curves: if $X$ and $Y$ are curves, G is a finite reducible group and $Y = X/G$, then we can write $K_G(X)$ in terms of $K(Y)$ and some representation rings associated to the group. Prof. Dhillon and I have generalized this result to any dimension using the description of the category of coherent sheaves on a root stack given by Borne and Vistolli.