  In this paper we consider dynamical r-matrices over a nonabelian base. There
are two main results. First, corresponding to a fat reductive decomposition of
a Lie algebra $\frakg =\frakh \oplus \frakm$, we construct geometrically a
non-degenerate triangular dynamical r-matrix using symplectic fibrations.
Second, we prove that a triangular dynamical r-matrix $r: \frakh^* \lon
\wedge^2 \frakg$ corresponds to a Poisson manifold $\frakh^* \times G$. A
special type of quantizations of this Poisson manifold, called compatible star
products in this paper, yields a generalized version of the quantum dynamical
Yang-Baxter equation
  (or Gervais-Neveu-Felder equation). As a result, the quantization problem of
a general dynamical r-matrix is proposed.
