A colorless c-cbar dipole emerging from a heavy ion collision and developing the charmonium wave function can be broken-up by final state interactions (FSI) propagating through the hot medium created in the collision. We single out two mechanisms of charmonium attenuation: (i) Debye color screening, called melting; and (ii) color-exchange interaction with the medium, called absorption. The former problem has been treated so far only for charmonia at rest embedded in the medium, while in practice their transverse momenta at the LHC are quite high, <p_T^2>=7-10 GeV^2. We demonstrate that a c-cbar dipole may have a large survival probability even at infinitely high temperature. We develop a procedure of Lorentz boosting of the Schroedinger equation to a moving reference frame and perform the first realistic calculations of the charmonium survival probability employing the path-integral technique, incorporating both melting and absorption. These effects are found to have comparable magnitudes. We also calculated the FSI suppression factor for the radial excitation psi(2S) and found it to be stronger than for J/psi, except large p_T, where psi(2S) is relatively enhanced. The azimuthal asymmetry parameter v_2 is also calculated.
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