  Cuspidal representations of a reductive p-adic group G over a field of
characteristic different from p are relatively injective and projective with
respect to extensions that split by a U-equivariant linear map for any subgroup
U that is compact modulo the centre. The category of smooth representations
over a field whose characteristic does not divide the pro-order of G is the
product of the subcategories of cuspidal representations and of
subrepresentations of direct sums of parabolically induced representations.
