Real C*-Algebras, United KK-Theory, and the Universal Coefficient Theorem

We define united KK-theory for real C*-algebras A and B such that A is separable and B is σ-unital, extending united K-theory in the sense that KK CRT (R, B) = K CRT (B).United KK-theory contains real, complex, and self-conjugate KK-theory; but unlike unaugmented real KK-theory, it admits a universal coefficient theorem.For all separable A and B in which the complexification of A is in the bootstrap category, KK CRT (A, B) can be written as the middle term of a short exact sequence whose outer terms involve the united K-theory of A and B. As a corollary, we prove that united K-theory classifies KKequivalence for real C*-algebras whose complexification is in the bootstrap category.