  We define united KK-theory for real C*-algebras A and B such that A is
separable and B is sigma-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 KK-equivalence for real C*-algebras whose complexification is in the
bootstrap category.
