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@Johannes I've looked at Karoubi's book and I'm not sure whether you've misunderstand his definition of $K^{p,q}$. In his Definition II 2.13 and Definition III 4.11, $K^{p,q}(X)$ should be constructed by triples $(E,F, \eta)$ instead of $(E, eta_0, \eta_1)$. Hopefully this helps.
