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A-modules abelian algebraic K-theory assume bijective canonical Chern classes classifying space coefficients cohomology commutative diagram complex composition conductor congruence subgroup consider construction Corollary corresponding CW-complex defined definition denote Edited element equivariant etale exact sequence extension fibration field finite group functor G-map given group G H-space hence homology homomorphism homotopy equivalence induced injective integer inverse irreducible isomorphism K-groups kernel Lecture Notes Lemma Let F Let G linear group matrix Milnor modules morphism natural map natural transformation notation Notes in Math obtain orthogonal pair polynomial prime projective projective modules Proof Proposition prove Quillen relations representations resp result ring Rn(b satisfies semi-local semi-local ring simplicial set spectral sequence Springer-Verlag St(R stability Steinberg group suffices Suppose surjective symbol Theorem theory topological trivial unimodular universal vector zero