A decomposition formula for equivariant stable homotopy classes

Abstract

For any compact Lie group $G$, we give a decomposition
of the group $\{X,Y\}_G^k$ of (unpointed) stable $G$-homotopy
classes as a direct sum of subgroups of fixed orbit types.
This is done by interpreting the $G$-homotopy classes
in terms of the generalized fixed-point transfer
and making use of conormal maps.