  We prove the Kirillov-Reshetikhin (KR) conjecture in the general case : for
all twisted quantum affine algebras we prove that the characters of KR modules
solve the twisted Q-system and we get explicit formulas for the character of
their tensor products (the untwisted simply-laced case was treated by Najakima,
and the untwisted case by the author). The proof is uniform and provides
several new developments for the representation theory of twisted quantum
affine algebras, including twisted Frenkel-Reshetikhin q-characters (expected
by Frenkel-Reshetikhin and Frenkel-Mukhin). We also prove the twisted T-system.
As an application we get explicit formulas for the twisted q-characters of
fundamental representations for all types, including the formulas for types
D_4^{(3)}, E_6^{(2)} conjectured by Reshetikhin. We prove the formulas for KR
modules in types A_n^{(2)} and D_4^{(3)} conjectured by Kuniba-Suzuki.
Eventually our results imply the conjectural branching rules [HKOTT] to the
quantum subalgebra of finite type.

Quantum Algebra;Representation Theory