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We construct the action of the quantum double of $\uq$ on the standardPodle\'s sphere and interpret it as the quantum projective formula generalizingto the q-deformed setting the action of the Lorentz group of global conformaltransformations on the ordinary Riemann sphere.Comment: LaTeX, 16 pages, we add a reference where an alternative construction  of the q-Lorentz group action on the Podles sphere is give

q -deformation of z→(αz+β)/(γz+δ)