  We study the t-structure induced by an n-tilting module T in the derived
category D(R) of a ring R. Our main objective is to determine when the heart of
the t-structure is a Grothendieck category. We obtain characterizations in
terms of properties of the module category over the endomorphism ring of T and
as a main result we prove that the heart is a Grothendieck category if and only
if T is a pure projective $R$-module.
