This is the second part of a two-part paper developing the module theo
ry, and a theory of complexity and varieties for modules, in the conte
xt of Kropholler's class of groups LHF. The numbering is a continuatio
n of the numbering for the first part [D. J. Benson, J. Algebra (1997)
, 260-287]. (C) 1997 Academic Press.