  O'Grady's generalized Franchetta conjecture (GFC) is concerned with
codimension 2 algebraic cycles on universal polarized K3 surfaces. In
\cite{BL17}, this conjecture has been studied in the Betti cohomology groups.
Following a suggestion of Voisin, we investigate this problem in the
Deligne-Beilinson (DB) cohomology groups. In this paper, we develop the theory
of Deligne-Beilinson cohomology groups on separated (smooth) Deligne-Mumford
stacks. Using the automorphic cohomology group and Noether-Lefschetz theory, we
compute the 4-th DB-cohomology group of universal oriented polarized K3
surfaces with at worst an $A_1$-singularity and show that GFC for such family
holds in DB-cohomology. In particular, this confirms O'Grady's original
conjecture in DB cohomology.
