Power operations in orbifold Tate $K$-theory

Abstract

We formulate the axioms of an orbifold theory with power operations. We define orbifold Tate $K$-theory, by adjusting Devoto’s definition of the equivariant theory, and proceed to construct its power operations. We calculate the resulting sym- metric powers, exterior powers and Hecke operators and put our work into context with orbifold loop spaces, level structures on the Tate curve and generalized Moonshine.