  We study the Grothendieck classes of quiver cycles, i.e. invariant closed
subvarieties of the representation space of a quiver. For quivers without
oriented loops we show that the class of a quiver cycle is determined by quiver
coefficients, which generalize the earlier studied quiver coefficients for
equioriented quivers of type A. We conjecture that quiver coefficients satisfy
positivity and finiteness properties. Our main result is a formula for the
quiver coefficients for orbit closures of Dynkin type with rational
singularities, which confirms the finiteness conjecture. This formula is based
on Reineke's desingularization of such orbit closures. For quivers of type A3,
we give positive combinatorial formulas for the quiver coefficients, which
confirm the full conjecture. We also interpret quiver coefficients as formulas
for degeneracy loci defined by quivers of vector bundle maps.
