  We consider the Poisson algebra S(M) of smooth functions on T^*M which are
fiberwise polynomial. In the case where M is locally projectively (resp.
conformally) flat, we seek the star-products on S(M) which are SL(n+1,R) (resp.
SO(p+1,q+1))-invariant. We prove the existence of such star-products using the
projectively (resp. conformally) equivariant quantization, then prove their
uniqueness, and study their main properties. We finally give an explicit
formula for the canonical projectively invariant star-product.
