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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 numberdifferent from p. We describe the block decomposition of the category of finitelength smooth representations of G with coefficients in an algebraically closedfield of characteristic l. Unlike the case of complex representations of anarbitrary p-adic reductive group and that of l-modular representations ofGL(n,F), several non-isomorphic supercuspidal supports may correspond to thesame block. We describe the (finitely many) supercuspidal supportscorresponding to a given block. We also prove that a supercuspidal block isequivalent to the principal (that is, the one which contains the trivialcharacter) block of the multiplicative group of a suitable division algebra,and we determine those irreducible representations having a nontrivialextension with a given supercuspidal representation of G.

Block decomposition of the category of l-modular smooth representations of finite length of GL(m,D)