Equivariant Infinite Loop Spaces

Generalized cohomology theories such as singular cohomology and topological K-theory can be represented by spectra. (Connective spectra can be described at the space level by infinite loop spaces. In this talk we will describe equivariant infinite loop spaces which come up in the study of generalized equivariant cohomology theories such as equivariant K-theory. When the group acting  G is finite, Costenoble and Waner showed that group like equivariant E_infty - spaces model equivariant infinite loop spaces. .................contd...... Following Segal's work, we give a construction of Gamma-soaces (and hence equivariant infinite loop spaces) starting from symmetric monoidal G-categories where G is a finite group.