Power operations in orbifold Tate K-theory

TL;DR

This paper develops an orbifold Tate K-theory framework with power operations, connecting it to orbifold loop spaces, level structures, and Moonshine phenomena, and computes key algebraic operations within this setting.

Contribution

It introduces a new axiomatic orbifold theory with power operations and constructs orbifold Tate K-theory, extending Devoto's equivariant theory and computing its algebraic operations.

Findings

Defined orbifold Tate K-theory with power operations

Calculated symmetric and exterior powers, Hecke operators

Connected theory to orbifold loop spaces and Moonshine

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 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.