The fluorescence excitation spectrum of the BKr van der Waals complex in the vicinity of the B atomic 2s2p(22)D <-- 2s(2)2p P-2 transition is reported. A vibrational progression in this spectrum is assigned to the D-2 Pi <-- X-2 Pi(1/2) transition, in analogy with BAr. The lifetimes of BKr(D-2 Pi) vibrational levels are considerably smaller than the B(2s2p(22)D) atomic lifetime, indicative of an excited state predissociation. From the observed threshold for B(2s2p(22)D) + Kr continuum excitation, we obtain estimates of the BKr dissociation energies for the ground X-2 Pi(1/2) (D-0 " = 159.4 +/- 1.2 cm(-1)) and the excited D-2 Pi (D-0’ = 120.6 +/- 1.2 cm(-1)) states. Two weak bands recorded in the same spectral region are tentatively assigned to the E-2 Sigma(+) <-- X-2 Pi(1/2)? transition. In the spectral region around the B atomic 2s(2)3s S-2 <-- 2s(2)2p P-2 transition to the lowest Rydberg state, no bands assignable to diatomic BKr are found, in contrast to the BNe and BAr systems. Instead, complicated fluorescence excitation features are observed, and these are believed to be due to excitation of higher BKr, clusters. It appears that both the B-2 Sigma(+) and C-2 Delta states of BKr do not fluoresce because of predissociation through spin-orbit coupling to a repulsive quarter state.