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We find the bosonic sector of the gauged supergravities that are obtainedfrom 11-dimensional supergravity by Scherk-Schwarz dimensional reduction withflux to any dimension D. We show that, if certain obstructions are absent, theScherk-Schwarz ansatz for a finite set of D-dimensional fields can be extendedto a full compactification of M-theory, including an infinite tower ofKaluza-Klein fields. The internal space is obtained from a group manifold(which may be non-compact) by a discrete identification. We discuss thesymmetry algebra and the symmetry breaking patterns and illustrate these withparticular examples. We discuss the action of U-duality on these theories interms of symmetries of the D-dimensional supergravity, and argue that ingeneral it will take geometric flux compactifications to M-theory onnon-geometric backgrounds, such as U-folds with U-duality transition functions.Comment: Latex, 47 page

Flux compactifications of M-theory on twisted tori