Title: Deformations with respect to an algebraic group. Abstract: This is joint work with Ted Chinburg. We study deformations of positive characteristic representations of a profinite group into a specified smooth algebraic group G over the p-adic integers. The corresponding G-deformation functor is a generalization of the deformation functor studied by Mazur. We show that the G-deformation functor has a universal deformation ring for representations whose endomorphisms are given by scalars. When G is an orthogonal group, this leads to studying universal versions of results of Serre, Frohlich and Saito about the connection of Stiefel-Whitney classes and Hasse-Witt invariants of orthogonal Galois representations.