  We introduce a family of tableaux that simultaneously generalizes the
tableaux used to characterize Grothendieck polynomials and k-Schur functions.
We prove that the polynomials drawn from these tableaux are the affine
Grothendieck polynomials and k-K-Schur functions -- Schubert representatives
for the K-theory of affine Grassmannians and their dual in the nil Hecke ring.
We prove a number of combinatorial properties including Pieri rules.
