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# Homology, Homotopy and Applications

## Volume 15 (2013)

### Number 1

### Power operations in orbifold Tate $K$-theory

Pages: 313 – 342

DOI: https://dx.doi.org/10.4310/HHA.2013.v15.n1.a16

#### Author

#### 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.

#### Keywords

elliptic cohomology, Tate curve, cohomology operation, level structure, generalized moonshine

#### 2010 Mathematics Subject Classification

19Lxx

Published 1 May 2013