Given a Coxeter group and a standard parabolic subgroup, Deodhar constructed a module over the Iwahori-Hecke algebra of the Coxeter group, giving rise to the so-called parabolic Kazhdan-Lusztig polynomials. There is no general theory of "Coxeter subgroups" of Coxeter groups, but several families of subgroups of Coxeter groups themselves admit a canonical structure of Coxeter group. We explain how to generalize Deodhar's construction to subgroups obtained as fixed points of an automorphism of order at most two of a standard parabolic subgroup of an arbitrary Coxeter group. This is joint work with P.-E. Chaput and L. Fresse, relying on properties of elements of minimal length in cosets modulo such subgroups obtained in a joint work with N. Chapelier.