Abstract: This is a report on a joint work with Anastasia Stavrova (St Petersburg). For a group scheme G over a ring A, we define the R-equivalence on G(A) in a compatible way with the case of algebraic groups. We compute the invariant G(A)/R in the case of a local ring when G is a torus or G is isotropic semisimple simply connected.
Ref: P. Gille and A. Stavrova, R-Equivalence on Group Schemes
