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There exists an explicit combinatorial formula for the characters of the symmetric group in terms of ribbon tableaux, called the Murnaghan-Nakayama rule. A simple proof of this rule due to Fomin and Greene uses symmetric functions in noncommutative variables. In this talk we will investigate the power of this approach and also show how it can be applied to find a Murnaghan-Nakayama rule associated to the affine Grassmannian and explicit formulas for fusion/quantum cohomology coefficients.