Abstract: The generalized character map of Hopkins, Kuhn, and Ravenel [9] can be interpreted as a map of cohomology theories beginning with a height n cohomology theory E and landing in a height 0 cohomology theory with a rational algebra of coefficients that is constructed out of E .We use the language of p -divisible groups to construct extensions of the generalized character map for Morava E -theory to every height between 0 and n. 55N20; 55N91We provide motivation and summarize the main result.Let K be a complex K -theory and let R.G/ be the complex representation ring of a finite group G .Consider a complex representation of G as a G -vector bundle over a point.Then there is a natural map R.G/ !K 0 .BG/.This takes a virtual representation to a virtual vector bundle over BG by applying the Borel construction EG G .It is a special case of the Atiyah-Segal completion theorem [2] from the 60s that this map is an isomorphism after completing R.G/ with respect to the ideal of virtual bundles of dimension 0.Let L be a minimal characteristic zero field containing all roots of unity, and let Cl.GI L/ be the ring of class functions on G taking values in L. A classical result in representation theory states that L is the smallest field such that the character map R.