Quasi-theories and their equivariant orthogonal spectra

TL;DR

This paper develops a method to construct orthogonal G-spectra for quasi-theories related to certain cohomology theories, enabling new approaches in equivariant stable homotopy theory.

Contribution

It introduces a construction of orthogonal G-spectra for quasi-theories, extending the framework for equivariant cohomology theories.

Findings

Constructed orthogonal G-spectra for quasi-theories up to weak equivalence.

Applied the construction specifically to quasi-elliptic cohomology.

Provides a foundation for further development of equivariant cohomology theories.

Abstract

In this paper we construct orthogonal $G-$spectra up to a weak equivalence for the quasi-theory $QE_{n, G}^*(-)$ corresponding to certain cohomology theories $E$. The construction of the orthogonal $G-$spectrum for quasi-elliptic cohomology can be applied to the constructions for quasi-theories.