^ is a finite group, n the category of finite (left) z-sets, S a q-set, ~ the associated category (see i.i), and Q an exact category in the sense of Quillen [9]. We show that the category [~,Q] of functors from S to Q is also exact and then define KW(S,Q) as the = n n th algebraic K-group associated with [~,Q] , K~(S,Q,T) as n th the algebraic K-group associated with the category [~,Q] with respect to T-exact sequences (see 2 I) where T is any H-set, and PZ(S,Q,T) as • n