  We calculate the intershell resistance R_{21} in a multiwall carbon nanotube
as a function of temperature T and Fermi level (e.g. a gate voltage), varying
the chirality of the inner and outer tubes. This is done in a so-called Coulomb
drag setup, where a current I_1 in one shell induces a voltage drop V_2 in
another shell by the screened Coulomb interaction between the shells neglecting
the intershell tunnelling. We provide benchmark results for R_{21}=V_2/I_1
within the Fermi liquid theory using Boltzmann equations. The band structure
gives rise to strongly chirality dependent suppression effects for the Coulomb
drag between different tubes due to selection rules combined with mismatching
of wave vector and crystal angular momentum conservation near the Fermi level.
This gives rise to orders of magnitude changes in R_{21} and even the sign of
R_{21} can change depending on the chirality of the inner and outer tube and
misalignment of inner and outer tube Fermi levels. However for any tube
combination, we predict a dip (or peak) in R_{21} as a function of gate
voltage, since R_{21} vanishes at the electron-hole symmetry point. As a
byproduct, we classified all metallic tubes into either zigzag-like or
armchair-like, which have two different non-zero crystal angular momenta m_a,
m_b and only zero angular momentum, respectively.
