2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155803Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple on this sphere with a Dirac operator which is isospectral to the canonical one on the round undeformed four-sphere and which gives metric dimension four for the noncommutative geometry. 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.40 pages, no figures, Latex. v2: Title changed. Sect. 9 on real structure completely rewritten and results strengthened. Additional minor changes throughout the paperQuantum AlgebraHigh Energy Physics - Theory58B32; 58B34text