We equip the multi-pullback C*-algebra C(S 5 H) of a non-commutative deformation of the 5-sphere with a free U (1)-action, and show that its fixed-point subalgebra is isomorphic with the C*-algebra of the multi-pullback quantum complex projective plane. Our main result is the stable nontriviality of the dual tautological line bundle associated to the action. We prove it by combining Chern-Galois theory with the Milnor connecting homomorphism in K-theory. Using the Mayer-Vietoris six-term exact

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... equences and the functoriality of the Künneth formula, we also compute the K-groups of C(S 5 H).