Topological K-theory of Equivariant Singularity Categories
  We study the topological K-theory spectrum of the dg singularity category associated to a weighted projective complete intersection. We calculate the topological K-theory of the dg singularity category of a weighted projective hypersurface in terms of its Milnor fiber and monodromy operator, and, as an application, we obtain a lift of the Atiyah-Bott-Shapiro construction to the level of spectra. 
Michael K. Brown, Tobias Dyckerhoff
math.AG math.KT