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Given C^*-algebras A and B and a ^*-homomorphism: A B, we develop a portrait of the relative K-theory K_* () using an approach due to Karoubi. This development gives rise to certain six-term exact sequences. We show that the theory so obtained is naturally isomorphic to the K-theory of the mapping cone of.
Mitch Haslehurst (Thu,) studied this question.