In this talk, I will present the notion of affine Weyl groups and Kazhdan-Lusztig cells. Then, using a geometric presentation of an affine Weyl group, I will establish that the Kazhdan-Lusztig polynomials are invariant under (long enough) translations. This, plus some computations with GAP, will allow us to determine the decomposition of affine Weyl group of type G2 into left cells, for certain choice of parameters.