  We study relations between the two-parameter $\U_q(sl(n))$-invariant
deformation quantization on $sl^*(n)$ and the reflection equation algebra. The
latter is described by a quantum permutation on $\End(\C^n)$ given explicitly.
The reflection equation algebra is used for constructing the one-parameter
quantization on coadjoint orbits, including symmetric and certain bisymmetric
and nilpotent ones. Our approach is based on embedding the quantized function
algebras on the orbits into the algebra of functions on the quantum group
$SL_q(n)$ via reflection equation algebra characters.
