### 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.

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.

#### Keywords

Equivariant stable homotopy groups; equivariant fixed-point transfer

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