  We prove a result which provides a link between the decomposition of
parabolically induced representations and the Bushnell--Kutzko theory of
typical representations. As an application, we show that there exists a
well-defined inertial Langlands correspondence which respects the monodromy
action of L-parameters, under some standard conjectures regarding the local
Langlands correspondence. To allow for potential applications of this inertial
Langlands correspondence, we also provide a complete construction of the set of
typical representations, giving a parametrization of these in terms of the
structure of the Bruhat--Tits building of $G$.
