On product type actions of G_q

We will study a faithful product type action of G_q that is the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of G_q. This enables us to classify product type actions of SU_q(2) up to conjugacy. We also compute the intrinsic group of G_{q,\Omega}, the 2-cocycle deformation of G_q that is naturally associated with the quantum flag manifold T\backslash G_q.