The involution on the equivariant Whitehead group

For a finite group G we define an involution on the equivariant Whitehead group given by reversing the direction of an equivariant h-cobordism. It turns out that the involution is not compatible with the splitting of the equivariant Whitehead group into a direct sum of algebraic Whitehead groups, certain correction terms involving the transfer maps of the normal sphere bundles of the various fixed point sets come in. However, if the group has odd order, these transfer maps all vanish. We prove a duality formula for a G-homotopy equivalence (f f): (M; M) (N, N) relating the equivariant Whitehead torsion of f and (f,f).