  We study spectrum of D=2 N=(2,2) QED with N+1 massive charged chiral
multiplets, with care given to precise supermultiplet countings. In the
infrared the theory flows to CP^N model with twisted masses, where we construct
generic flavored kink solitons for the large mass regime, and study their
quantum degeneracies. These kinks are qualitatively different and far more
numerous than those of small mass regime, with features reminiscent of
multi-pronged (p,q) string web, complete with the wall-crossing behavior. It
has been also conjectured that spectrum of this theory is equivalent to the
hypermultiplet spectrum of a certain D=4 Seiberg-Witten theory. We find that
the correspondence actually extends beyond hypermultiplets in D=4, and that
many of the relevant indices match. However, a D=2 BPS state is typically
mapped to several different kind of dyons whose individual supermultiplets are
rather complicated; the match of index comes about only after summing over
indices of these different dyons. We note general wall-crossing behavior of
flavored BPS kink states, and compare it to those of D=4 dyons.
