the partition algebra is the centralizer of the symmetric group acting on tensor powers of its natural (permutation) module. it has a diagrammatic basis that generalizes brauer's centralizer algebra for the orthogonal group. many of these diagram centralizer algebras have q-generalizations: for example the q-symmetric group is the iwahori-hecke algebra and the q-brauer algebra is the bmw algebra. we will introduce a candidate for a q-partition algebra --- constructed using harish-chandra restriction and induction on the finite general linear group over a field with q elements --- and we will illustrate some preliminary computations in this algebra.