Hadronic tensor molecule <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si18.svg"> <mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mi>c</mml:mi> <mml:mrow> <mml:mo>*</mml:mo> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> <mml:msubs

Mass and full decay width of the hadronic tensor molecule MT=Bc*+Bc*− with spin-parities JPC=2++ are examined in the framework of QCD sum rule method. To find the mass m and current coupling Λ of this state, we use the two-point sum rules. The result (12.87 ± 0.08) GeV for m indicates that MT can easily decay to pairs of J/ψΥ, ηbηc, Bc+Bc−, and Bc*+Bc*− mesons. Kinematically permitted ways for MT to transform to conventional mesons include also processes MT→D(*)+D(*)−, D(*)0D‾(*)0, and Ds(*)+Ds(*)− triggered by annihilation of bb‾ quarks in the molecule. The decays to meson pairs B(*)+B(*)−, B(*)0B‾(*)0, and Bs(*)0B‾s(*)0 generated by cc‾→ light quarks are also among possible channels of the hadronic molecule MT. Technical tools of the three-point sum rule approach are applied to compute partial widths of these decays. Our results for the mass and width ΓMT=(154±19)MeV of the tensor molecule MT are important for experimental studies of fully heavy exotic structures.