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Open problems
Despite these successes, RR fluxes are not quite classified by K-theory.
Diaconescu, Moore & Witten (2003) argued that the K-theory classification is incompatible with S-duality in IIB string theory.

In addition, if one attempts to classify fluxes on a compact ten-dimensional spacetime, then a complication arises due to the self-duality of the RR fluxes.
The duality uses the Hodge star, which depends on the metric and so is continuously valued and in particular is generically irrational.
Thus not all of the RR fluxes, which are interpreted as the Chern characters in K-theory, can be rational.
However Chern characters are always rational, and so the K-theory classification must be replaced.
One needs to choose a half of the fluxes to quantize, or a polarization in the geometric quantization-inspired language of Diaconescu, Moore, and Witten and later of Varghese & Sati (2004).
Alternately one may use the K-theory of a 9-dimensional time slice as has been done by Maldacena, Moore & Seiberg (2001).
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