Hecke algebras and class-group invariants

Let G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, psi, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]), Alternative constructions of Chinburg invariants arising from the Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of psi. As an application we show that two such constructions coincide.