While writing a grant proposal I faced a problem of justification my area of interest to a broader audience. So I thought it would be nice to ask it here:
What are applications/impact of computations in $RO(G)$-graded cohomology theories such as Bredon cohomology or equivariant K-theory outside of homotopy theory?
To shed more light on the question - the first answer which comes to mind is Hill-Hopkins-Ravenel work on Kervaire invariant problem. They used equivariant homotopy theory and, in particular, $RO(G)$-graded homotopy groups of some spectra to solve problem of geometric nature, or at least arising from geometric topology.
So the question is about areas (for example number theory, representation theory, geometric topology) where $RO(G)$-graded information can be used to bring new approaches or solve old problems in a way not previously explored.
Thank you very much!
