  We construct a topological charge of gauge field configurations on a fuzzy
S^2xS^2 by using a Dirac operator satisfying the Ginsparg-Wilson relation. The
topological charge defined on the fuzzy S^2xS^2 can be interpreted as a
noncommutative (or matrix) generalization of the 2nd Chern character on
S^2xS^2. We further calculate the number of chiral zero modes of the Dirac
operator in topologically nontrivial gauge configurations. Generalizations of
our formulation to fuzzy (S^2)^k are also discussed.

High Energy Physics - Theory;High Energy Physics - Lattice