Let F be a 2-regular graph of order v. The Oberwolfach problem,
OP(F), asks for a 2-factorization of the complete graph on v vertices in
which each 2-factor is isomorphic to F. In this paper, we give a complete
solution to the Oberwolfach problem over infinite complete graphs, proving the
existence of solutions that are regular under the action of a given involution
free group G. We will also consider the same problem in the more general
contest of graphs F that are spanning subgraphs of an infinite complete graph
K and we provide a solution when F is locally finite. Moreover, we
characterize the infinite subgraphs L of F such that there exists a
solution to OP(F) containing a solution to OP(L)