For a split reductive group ${ }^L G$ over a global field, we determine the spectrum of the spherical Hecke algebra coming from the unramified Eisenstein series for the minimal parabolic ${ }^L B$. This is done using a certain decomposition of the Springer stack $T^*(B \backslash G/ B)$ for the Langlands dual group in the additive group of cobordisms of cohomologically proper derived quotient stacks.
Categories: math.NT math.AG math.AT math.RT