This may be a silly question but I don't know the answer.


I know the construction of (equivariant) K-spectrum $KU\_G$ and the periodicity of (equivariant) K-theory. But I don't know its structure maps and how they are constructed.


Can anybody show me the answer or some reference on this? Thanks very much.



The structure map of topological K-theory
That is a very reasonable question. By a $G$-spectrum $KU\_G$, $G$ a compact Lie group, one should mean a genuine $G$\_spectrum, so suitably indexed on representations of $G$. One gets the structure maps by use of equivariant Bott periodicity. A good sketch of how this goes, without full details, is given on pages 146-148 of Equivariant Homotopy and Cohomology Theory (available here: <http://www.math.uchicago.edu/~may/BOOKS/alaska.pdf>). The relevant chapter was written by John Greenlees. 


