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We identify the group of homomorphismsHom  GF    (  F  ,   RU  Q   )in the abelian category   GF   of (  fin  )‐global functors to the rationalization of the unitary representation ring functor    RU  Q   . The result is a certain inverse limit over the values of   F   at cyclic groups and we deduce that the higher   Ext  ‐groupsExt  GF  n    (  F  ,   RU  Q   )have to vanish for    n  ⩾  2   . This leads to a rational splitting of the (  fin  )‐global equivariant   K  ‐theory spectrum   KU   into a sum of Eilenberg–MacLane spectra. Interpreted in terms of cohomology theories, it means that the equivariant Chern character is compatible with restrictions along all group homomorphisms.

Rational extensions of the representation ring global functor and a splitting of global equivariant K ‐theory