I will explain the construction of "Gromov-Witten invariants for the quotient stack [point/GL(1)]", beginning with the definition of an appropriate moduli stack of marked curves and holomorphic line bundles (maps to [point/GL(1)]) and then explaining why this (non-separable, non-proper, non-finite type, non-Deligne-Mumford, and otherwise recalcitrant) moduli stack does indeed have well-defined K-theory invariants. If time permits, I'll indicate further generalizations to [X/G], for X proper, and G reductive. This talk is based on joint work with Edward Frenkel & Constantin Teleman.