  We construct a theory of local gamma factors for $G_2 \times GL_r$ using a
functorial lifting from $G_2$ to $GL_7$. This theory of gamma factors is
uniquely characterized by a usual list of properties, showing that it is the
only possible candidate. Moreover, this theory of gamma factors is compatible
with the Galois theoretic one under the local Langlands correspondence for
$G_2$.
