Regular Algebraic $K$-theory for groups -- Part I

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to a ring $R$ the (perfect>) commutator subgroup $E(R)$ of the infinitedimensional general linear group over $R$.