Residually finite dimensional C*-algebras and subquotients of the CAR algebra

It is proved that the cone of a separable nuclearly embeddable residually finite-dimensional C*-algebra embeds in the CAR algebra (the UHF algebra of type 20(infinity)). As a corollary we obtain a short new proof of Kirchberg's theorem asserting that a separable unital C*-algebra A is nuclearly embeddable if and only there is a semisplit extension 0 --> J --> E --> A --> 0 with E a unital C*-subalgebra of the CAR algebra and the ideal J an AF-algebra. The new proof does not rely on the lifting theorem of Effros and Haagerup.