Mitosis algorithm for Grothendieck polynomials

The goal of the present paper is to extend the mitosis algorithm, originally developed by Ezra Miller and Allen Knutson for the case of Schubert polynomials, to the case of Grothendieck polynomials. In addition we will also use this algorithm to construct a short combinatorial proof of Fomin-Kirillov's formula for the coefficients of Grothendieck polynomials.