Let ξ(t), t [0, 1], be a jump Lévy process. We denote by Pξ law of ξ in the Skorokhod space [0, 1]. Under some nondegeneracy condition on the Lévy measure Λ of the process, we construct a group of Pξ-preserving transformations of the space double-struck D sign[0, 1]. Bibliography: 11 titles. © 2007 Springer Science+Business Media, Inc.