The isospectral dirac operator on the 4-dimensional orthogonal quantum sphere

Equivariance under the action of U-q (so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S-q(4). These representations are the constituents of a spectral triple on S(q)(4)with a Dirac operator which is isospectral to the canonical one on the round sphere S-4 and which then gives 4(+)-summability. Non-triviality of the geometry is proved by pairing the associated Fredholm module with an 'instanton' projection. We also introduce a real structure which satisfies all required properties modulo smoothing operators.