STABLE CLASS OF EQUIVARIANT ALGEBRAIC VECTOR BUNDLES OVER REPRESENTATIONS Masuda, Mikiya;
Let G be a reductive algebraic group and let B, F be G-modules. We denote by (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor (B, ) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.