We study noncommutative maximal inequalities and ergodic theorems for group actions on von Neumann algebras. Consider a locally compact G of polynomial growth with symmetric subset V. Let ? be continuous action algebra M by trace-preserving automorphisms. then show that the operators defined Anx=1m(Vn)?Vn?gxdm(g),x?Lp(M),n?N,1?p??, are weak type (1,1) strong (p,p) 1<p<?. Consequently, sequence ...