  In this paper we generalize cellular algebras by allowing different partial
orderings relative to fixed idempotents. For these relative cellular algebras
we classify and construct simple modules, and we obtain other characterizations
in analogy to cellular algebras.
  We also give several examples of algebras that are relative cellular, but not
cellular. Most prominently, the restricted enveloping algebra and the small
quantum group for $\mathfrak{sl}_{2}$, and an annular version of arc algebras.
