Experimental results on the ωπ and ππ systems as observed in the pp annihilations at rest: pp→ω0π+π−

2400 events of the type pp → ω0π+π− are extracted from more than 10 000 five-body annihilations at rest: pp → 2π+2π−π0. The B meson is observed in the system (ωπ): its mass, width, and spin-parity are analyzed. Limits are given for the branching ratios B → φπ/B → ωπ and B → KK/B→ ωπ. It is necessary to introduce a structure in the (ππ) S-wave, I=0 amplitude to obtain a good interpretation of the data.