  Let F be a non-Archimedean locally compact field of residue characteristic p,
let G be an inner form of GL(n,F) with n>0, and let l be a prime number
different from p. We describe the block decomposition of the category of finite
length smooth representations of G with coefficients in an algebraically closed
field of characteristic l. Unlike the case of complex representations of an
arbitrary p-adic reductive group and that of l-modular representations of
GL(n,F), several non-isomorphic supercuspidal supports may correspond to the
same block. We describe the (finitely many) supercuspidal supports
corresponding to a given block. We also prove that a supercuspidal block is
equivalent to the principal (that is, the one which contains the trivial
character) block of the multiplicative group of a suitable division algebra,
and we determine those irreducible representations having a nontrivial
extension with a given supercuspidal representation of G.
