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We study magnetic properties of the half-filled Hubbard model on thetwo-dimensional $H_{00}$ hexagonal golden-mean quasiperiodic tiling. The tilingis composed of large and small hexagons, and parallelograms, and its vertexmodel is bipartite with a sublattice imbalance. The tight-binding model on thetiling has macroscopically degenerate states at $E = 0$. We find the existenceof two extended states in one of the sublattices, in addition to confinedstates in the other. This property is distinct from that of the well-knowntwo-dimensional quasiperiodic tilings such as the Penrose and Ammann-Beenkertilings. Applying the Lieb theorem to the Hubbard model on the tiling, weobtain the exact fraction of the confined states as $1/2\tau^2$, where $\tau$is the golden mean. This leads to a ferromagnetically ordered state in the weakcoupling limit. Increasing the Coulomb interaction, the staggered magneticmoments are induced and gradually increase. Crossover behaviour in themagnetically ordered states is also addressed in terms of perpendicular spaceanalysis.

Ferromagnetically ordered states in the Hubbard model on the $H_{00}$ hexagonal golden-mean tiling