  We prove the existence and uniqueness of a *projectively equivariant symbol
map*, which is an isomorphism between the space of bidifferential operators
acting on tensor densities over $R^n$ and that of their symbols, when both are
considered as modules over an imbedding of $sl(n+1,\R)$ into polynomial vector
fields. The coefficients of the bidifferential operators are densities of an
arbitrary weight. We obtain the result for all values of this weight, except
for a set of critical ones, which does not contain 0. In the case of second
order operators, we give explicit formulas and examine in detail the critical
values.
