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Abstract. The decomposition numbers in characteristic 2 of the groups of Ree type are determined, as well as the Loewy and socle series of the indecomposable projective modules. Moreover, we describe the Green correspondents of the simple modules. As an application of this and similar works on other simple groups with an abelian Sylow 2-subgroup, all of which have been classified apart from those considered in the present paper, we show that the Loewy length of an indecomposable projective module in the principal block of any finite group with an abelian Sylow 2-subgroup of order 2" is bounded by max{2n + 1, 2"}. This bound is the best possible.Introduction. The purpose of this paper is to determine the algebra structure of the principal 2-blocks B of the simple groups R(q) of Ree type of order \R(q)\ = (q3 + \)q\q -1), where q = 32n+1, and n = 1, 2,_ Let (F, R, S) be a splitting 2-modular system for R(q), where F has characteristic 2, and S and R have characteristic zero. The character table of the groups R(q) was determined by Ward [15] up to a few but very essential values missing because of the incomplete classification of these groups. Ward [15] also showed that B contains eight ordinary irreducible characters £" all of height zero, and five nonisomorphic simple FR(q)-moàxx\cs op,, i = 1,2,..., 5, where