Cohomology of the moduli stack of algebraic vector bundles

Let $\mathscr{ V}\mathrm{ ect}_n$ be the moduli stack of vector bundles of rank $n$ on schemes. We prove that, if $E$ is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies the projective bundle formula, then $E^*(\mathscr{ V}\mathrm{ ect}_{ n,S})$ is freely generated by Chern classes $c_1,\dotsc,c_n$ over $E^*(S)$ for any scheme $S$. Examples include all multiplicative localizing invariants.

Categories: math.AG math.AT math.KT