A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyalproduct-like deformations are naturally found for all FRT-models on coefficients and C 00 -functions. Strong rigidity (H^ = {0}) under deformations in the category of bialgebras is proved and consequences are deduced.

Several notions of invariance and covariance for * products with respect to Lie algebras and Lie groups are investigated. Some examples, including the Poincaré group, are given. The passage from the Lie-algebra invariance to the Lie-group covariance is performed. The compact and nilpotent cases are treated.

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