  In this paper we study the index theoretic interpretation of the analytical
assembly map that appears in the Baum-Connes conjecture. In its general form it
may be constructed using Kasparov's equivariant KK-theory. In the special case
of a torsionfree group the domain simplifies to the usual K-homology of the
classifying space BG of G and it is frequently used that in this case the
analytical assembly map is given by assigning to an operator an equivariant
index. We give a precise formulation of this statement and prove it.
