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We give an explicit combinatorial Chevalley-type formula for the equivariant K-theory of generalized flag varieties G/P which is a direct generalization of the classical Chevalley formula. Our formula implies a simple combinatorial model for the characters of the irreducible representations of G and, more generally, for the Demazure characters. This model, which we call the alcove path model, can be viewed as a discrete counterpart of the Littelmann path model, and has several advantages. Ourdoi:10.1093/imrn/rnm038 fatcat:x6ihahawi5ea3h5lbtr7isbbiq