The study of complex cobordism and related cohomology theories is a long standing and well respected area of algebraic topology. Another area has been that of (finite) group theoretic constructions, becoming, in its most modern form, equivariant stable homotopy theory. Results in recent years, most spectacularly the proofs of Segal's Burnside ring conjecture and Ravenel's nilpotence conjecture, have dramatically begun to bring to fruition these two branches of stable homotopy theory. Historically, these branches have been basically independent of each other. An exception is Atiyah's theorem relating K*(BG) (a bordism type of object) to the complex representation ring of G. There are now indications of much more widespread interrelations. This is the subject of Kuhn's recent and current research. It is hard to say where the study of such intricate algebraic patterns will lead, but the history of mathematics strongly suggests that mastering them will have repercussions elsewhere, either in use of the patterns themselves or of the techniques developed for treating them.
