Green Functors And Induction Theorems With General Coefficients

In this paper, let k be a commutative ring and G be a finite group. In the first part, let A be a Green functor for G over k, we prove that for a crossed G-monoid Γ, the Brauer construction of the Dress construction Ar has a simple form; We apply this conclusion to crossed Burnside rings and Hochschild cohomology rings and reprove some results of S.Bouc, S.Siegel and S.Witherspoon. In the second part, let k be a field of characteristic p(p is a prime), Rk(G) be the Brauer character ring of G and S be a subring of complex field C We prove an induction theorem for S(?)z Rk(G). We further determine the number of connected components of its prime spectrum.