  In this article we use the expansion for biquantization described in
Cattaneo-Felder [math.QA/0309180] for the case of symmetric spaces. We
introduce a function of two variables $E(X,Y)$ for any symmetric pairs. This
function has an expansion in terms of Kontsevich's diagrams. We recover most of
the known results though in a more systematic way by using some elementary
properties of this $E$ function. We prove that Cattaneo and Felder's star
product coincides with Rouviere's for any symmetric pairs. We generalize some
of Lichnerowicz's results for the commutativity of the algebra of invariant
differential operators and solve a long standing problem posed by M. Duflo for
the expression of invariant differential operators on any symmetric spaces in
exponential coordinates. We describe the Harish-Chandra homomorphism in the
case of symmetric spaces by using all these constructions. We develop a new
method to construct characters for algebras of invariant differential
operators. We apply these methods in the case of $\sigma$-stable polarizations.
