The p -typical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p -adically complete discrete valuation rings of characteristic 0 with residue field k and are universal in that sense. A. Dress and C. Siebeneicher generalized this construction by producing a functor \mathbf W_G attached to any profinite group G . The p -typical Witt vectors arise as those attached to the p -adic integers. Here we examine the ring structure of \mathbf W_G(k) for several examples of pro- p groups G and fields k of characteristic p . We will show that the structure is surprisingly more complicated than the p -typical case.