  We prove that the q-Schur algebras of finite type introduced in [LW22] are
cellular in the sense of Graham and Lehrer, which is a generalization of Geck's
theorem on the cellularity of Hecke algebras of finite type. Moreover, we study
special modules of the associated asymptotic Schur algebras and left cell
representations of Schur algebras, which generalize Lusztig's work about
special modules of asymptotic Hecke algebras and left cell representations of
Weyl groups, respectively.
