... identification of the K-theory of chain complexes of an additive categorywith the K-theory of the additive category is an Euler characteristic (see e.g.[9]).By abuse of notation we denote the category of ... [21, §3, §12] for the proof of part (i) for Lsor Lp. Part (ii) isdue to Bak for Lsand Lh[2], and is proved in [21, 12.1] for Lp. We can nowsubstitute this information into the Ranicki-Rothenberg ... ker(trfW1) ⊆ Lhn(ZG)(q).Proof. In [17] we localized at an odd prime p |G| in order to use theBurnside idempotents for all cyclic subgroups of G. The same proof works for the L-groups localized...