Classically the Chebotarev density theorem carries key arithmetical information about the splitting of divisors in Galois extensions of global fields. It is now a basic tool in arithmetic. The key ingredient in the standard proof is the Artin L-function.
Chapters 30 and 31 of [4] may be viewed as a motivic Chebotarev density theorem without motives. Indeed, in the last chapter the L-function of a Galois formula is studied and it is shown that it is "almost rational". This approach originated in [3].
In [2] we study motive valued L-functions. They specialise to Artin L-functions under the trace of Frobenius. We prove their basic properties. Using the ideas of [5] and [1, page 129] we settle questions about rationality of such functions. We define virtual motives that count points with prescribed Artin symbols. Using our rationality results we can derive formulas for these motives. These formulas can be viewed as a motivic Density theorem as they guarantee the existence of points of high degree with prescribe Artin symbol over a finite field.