  This is the first of two papers dedicated to the computation of the reduced
C*-algebra of a connected, linear, real reductive group up to Morita
equivalence, and the verification of the Connes-Kasparov conjecture for these
groups. These results were originally announced by Antony Wassermann in 1987.
In Part I we shall give details of the C*-algebraic Morita equivalence, and
then compute the Connes-Kasparov morphism subject to some results in tempered
representation theory that we shall prove in Part II using tools from David
Vogan's classification of the tempered dual.
