Power operations in orbifold Tate K-theory

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 symmetric 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.