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We formulate a Ginsparg-Wilson relation on a fuzzy 2-sphere for matter in theadjoint representation of the gauge group. Because of the Ginsparg-Wilsonrelation, an index theorem is satisfied. Our formulation is applicable totopologically nontrivial configurations as monopoles. It gives a solid basisfor obtaining chiral fermions, which are an important ingredient of thestandard model, from matrix model formulations of the superstring theory, suchas the IIB matrix model, by considering topological configurations in the extradimensions. We finally discuss whether this mechanism really works.

Ginsparg-Wilson relation on a fuzzy 2-sphere for adjoint matter