  We define even dimensional quantum spheres Sigma_q^2n that generalize to
higher dimension the standard quantum two-sphere of Podle's and the four-sphere
Sigma_q^4 obtained in the quantization of the Hopf bundle. The construction
relies on an iterated Poisson double suspension of the standard Podle's
two-sphere. The Poisson spheres that we get have the same symplectic foliation
consisting of a degenerate point and a symplectic plane and, after
quantization, have the same C^*-algebraic completion. We investigate their
K-homology and K-theory by introducing Fredholm modules and projectors.
