Hopf algebra orders in the group algebra of a finite group can be used to get information on the representation theory of the group. In this paper, we describe a class of such orders that arises from group valuations on the group and use properties of these orders to get a new bound on the degrees of the absolutely irreducible representations of the group. In Section 1, we discuss the basic properties of group valuations. A group valuation is a real-valued function on the group that satisfies conditions that reflect the product and commutator relations on the group. We also introduce weighted filtrations. These correspond to group valuations and are sometimes more convenient for computation. Next, Hopf algebra orders are introduced and in Section 3, their relation to group valuations is discussed. There is a one-one correspondence between group valuations satisfying certain conditions reflecting the orders of the group elements and the pth power map (the p-adic order-bounded group valuations) and certain Hopf algebra orders in the group algebra. An important invariant associated with a Hopf algebra order A is e(LA), where LA is the ideal of left integrals in A. In Section 4, we compute E(L~) for those Hopf algebra orders associated with p-adic orderbounded group valuations. In Section 5, we apply the results of Section 4 to get a new bound on the degrees of the absolutely irreducible representations of a finite group. In Section 6, we compare the bound given in Section 5 with the bound given in Ito’s theorem (the degree of an absolutely irreducible representation must divide the index of any normal abelian subgroup) for the groups of order 2”, 0 < n < 6. The work in the first six sections is all local; in Section 7, we briefly describe the global situation, and discuss some of the open questions involving Hopf algebra orders. In this paper, we assume that the reader is familiar with the results and techniques of [S]. Throughout this paper, K is an algebraic number field and