  We obtain a presentation of the t-deformed Grothendieck ring of a quantum
loop algebra of Dynkin type A, D, E. Specializing t at the the square root of
the cardinality of a finite field F, we obtain an isomorphism with the derived
Hall algebra of the derived category of a quiver Q of the same Dynkin type.
Along the way, we study for each choice of orientation Q a tensor subcategory
whose t-deformed Grothendieck ring is isomorphic to the positive part of a
quantum enveloping algebra of the same Dynkin type, where the classes of simple
objects correspond to Lusztig's dual canonical basis.
