Duality symmetry and the form fields of M-theory

In previous work we derived the topological terms in the M-theory action in terms of certain characters that we defined. In this note, we propose the extention of these characters to include the dual fields. The unified treatment of the M-theory four-form field strength and its dual leads to several observations. In particular we elaborate on the possibility of a twisted cohomology theory with a twist given by degrees higher than three.