For t in Nn, E.Miller has defined a category of t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if every generator x has a ≤ t. We compute the multigraded cohomologyand betti spaces of N k t (S/I) for every iterate k, and also the Smodule structure of the...