  The semi-stable ChowHa of a quiver with stability is defined as an analog of
the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in
equivariant Chow groups of semi-stable loci in representation varieties of
quivers. We prove several structural results on the semi-stable ChowHa, namely
isomorphism of the cycle map, a tensor product decomposition, and a
tautological presentation. For symmetric quivers, this leads to an
identification of their quantized Donaldson-Thomas invariants with the
Chow-Betti numbers of moduli spaces.
