Localisation and colocalisation of ehBtheory

The localisation of an R-linear triangulated category T at S −1 R for a multiplicatively closed subset S is again triangulated, and related to the original category by a long exact sequence involving a version of T with coefficients in S −1 R/R. We examine these theories and, under some assumptions, write the latter as an inductive limit of T with torsion coefficients. Our main application is the case where T is equivariant bivariant K-theory and R the ring of integers.