### Homology of linear groups via cycles in BG x X, by Kevin P. Knudson and Mark E. Walker

Let *G* be an algebraic group and let *X* be a smooth
integral scheme over a field *k*. In this paper we construct
homology-type groups Hi(*X,G*) by considering cycles
in the simplicial scheme B*G* x *X* (an idea suggested
by Andrei Suslin). We discuss the basic properties of these groups
and construct a spectral sequence, beginning with the groups
Hi(\Deltaj,G), which converges to the etale
cohomology of the simplicial group B*G*. These groups are
therefore connected with the study of Friedlander's generalized
isomorphism conjecture.

We also compute some examples, focusing in
particular on the case *X*=Spec(*k*). In the case where
*k* is the real numbers, there is a connection between the
groups Hi and the Z/2-equivariant cohomology of the
classifying space of the discrete group *G*(**R**).

Kevin P. Knudson <knudson@math.msstate.edu>

Mark E. Walker <mwalker@math.unl.edu>