Computation of the equivariant 1-stem

Let G be a compact Lie group. In this paper, combining a short exact sequence obtained by Balanov and Krawcewicz with some additional topological techniques, we complete the computation of the first equivariant stem π1Gst. Using the exact sequence and a property of nonabelian connected compact Lie groups, whose proof was suggested to us by R. Oliver, we show that this group is finite if and only if G is finite.