R-analogue of the Burnside ring of profinite groups and free Lie algebras

Let R be a finite-dimensional torsion-free special λ-ring. In this paper we generalize the results in Dress and Siebeneicher (Adv. in Math. 70 (1988) 89; 78 (1989) 1) by constructing R-analogue Ω̂R(G) of the Burnside ring of profinite groups Ω̂(G). In particular, we remark that the (Grothendieck) Lie-module denominator identity of free Lie algebras in Oh (Necklace rings and logarithmic functions, preprint, KIAS, 2003) is closely related to the canonical isomorphism between Ω̂R(G) and Grothendieck's ring of formal power series with coefficients in R and constant term 1.