I will demonstrate that motivic homotopy theory over the base field C, combined with classical machineries in algebraic topology such as the Serre spectral sequences, could produce interesting computations of Chow rings of classifying spaces.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/TopologySeminar