Haar Measure and the Artin Conductor

Let $G$ be a connected reductive group, defined over a local, non-archimedean field $k$. The group $G(k)$ is locally compact and unimodular. In On the motive of a reductive group, Invent. Math. 130 (1997), by B. H. Gross, a Haar measure $|\omega _G|$ was defined on $G(k)$, using the theory of Bruhat and Tits. In this note, we give another construction of the measure $|\omega _G|$, using the Artin conductor of the motive $M$ of $G$ over $k$. The equivalence of the two constructions is deduced from a result of G. Prasad.