Cellularity of the lowest two-sided ideal of an affine Hecke algebra

In this paper we show that the lowest two-sided ideal of an affine Hecke algebra is affine cellular for all choices of parameters. We explicitly describe the cellular basis and we show that the basis elements have a nice decomposition when expressed in the Kazhdan–Lusztig basis. In type A we provide a combinatorial description of this decomposition in term of number of paths.