Stable Grothendieck polynomials form a non-homogeneous basis for the ring of symmetric functions. They are the symmetric function analog of polynomial representatives for the K-theory of the Grassmannian. First defined by Fomin and Kirillov using divided difference operators, they have an alternative formulation in terms of set-valued tableaux due to Buch. Recently, there have been a plethora of papers exploring the combinatorics of stable Grothendieck polynomials. Building on this work, we will outline a proof of the Littlewood-Richardson rule for stable Grothendieck polynomials that is entirely combinatorial, without reference to the geometry of Grassmannians. This proof mirrors (and recovers) the jeu de taquin characterization of the Littlewood-Richardson rule for Schur functions. Speaker(s): Zachary Hamaker (University of Michigan)