  Let L be a non-archimedean local field of characteristic 0. We present a
variant of the theory of (\phi,\Gamma)-modules associated with Lubin-Tate
groups, developed by Kisin and Ren [Ki-Re], in which we replace the Lubin-Tate
tower by the maximal abelian extension \Gamma = Gal(L^ab/L). This variation
allows us to compute the functors of induction and restriction for
(\phi,\Gamma)-modules, when the ground field L changes. We also give a
self-contained account of the Cherbonnier-Colmez theorem on overconvergence in
our setting.
