Weak crossed product orders arising from partitions of a finite group

Let R be a complete discrete valuation ring with quotient field K, L a finite Galois extension of K with Galois group G and S the integral closure of R in L. In this article, using elements of the monoid Sl(G), the set of semilinear maps of G on the set of natural numbers introduced in [8], we construct certain crossed product orders in the case that the extension S/R is unramified. We associate an element of Sl(G) to every crossed product order and give a criterion for inflating idempotent 2-cocycles.