By a result of Kirchberg, every exact C*-algebra A can be embedded into a nuclear C*-algebra B. In fact, Kirchberg and Phillips later proved that the nuclear C*-algebra B can always be taken to be the Cuntz algebra on two generators. However, in general, the nuclear embeddings that are guaranteed to exist by the above results can be difficult to realize. Additionally, the image of an exact C*-algebra under a nuclear embedding can be relatively small and, consequently, properties like simplicity and primeness are not necessarily reflected in the larger C*-algebra. Hence, for a given exact C*-algebra, it is natural to seek for a more canonical nuclear embedding. In this direction, Ozawa proved that the reduced C*-algebra C_r*(F_n) of the free group F_n on n generators can be embedded into a nuclear C*-algebra that is contained in the injective envelope of C_r*(F_n). This provides a rather “tight” nuclear embedding of the reduced C*-algebra C_r*(F_n). He furthermore conjectured that it should be possible to construct such an embedding for any exact C*-algebra. We prove Ozawa’s conjecture for the reduced C*-algebra of every discrete exact group. This is joint work with Matthew Kennedy.