Witt vectors and equivariant ring spectra applied to cobordism

Given a finite group G we show that Dress and Siebeneicher'sring of G-typical Witt vectors on the Lazard ring, that is,on the polynomial ring on countably many indeterminates overthe integers, embeds as a subring of the unitary cobordism ringof G-manifolds. We also show that the ring of G-typical Wittvectors on the Lazard ring embeds as a subring of the ring ofhomotopy groups of the G-fixed point spectrum of the spectrumMU representing cobordism. The above results are derived byexploiting the interaction between restriction, additive transferand multiplicative transfer. This interaction is described bytwo Mackey functors satisfying a distributivity relation encodedin a formalism developed by Tambara.