  We take some initial steps towards illuminating the (hypothetical) $p$-adic
local Langlands functoriality principle relating Galois representations of a
$p$-adic field $L$ and admissible unitary Banach space representations of
$G(L)$ when $G$ is a split reductive group over $L$. The outline of our work is
derived from Breuil's remarkable insights into the nature of the correspondence
between 2-dimensional crystalline Galois representations of the Galois group of
$\Qdss_p$ and Banach space representations of $GL_{2}(\Qdss_p)$.
