  We propose, within the effective one body (EOB) approach, a new, resummed,
analytical representation of the gravitational wave energy flux absorbed by a
system of two circularized (nonspinning) black holes. This expression is such
to be well-behaved in the strong-field, fast motion regime, notably up to the
EOB-defined last unstable orbit. Building conceptually upon the procedure
adopted to resum the multipolar asymptotic energy flux, we introduce a {\it
multiplicative} decomposition of the multipolar absorbed flux made by three
factors: (i) the leading-order contribution, (ii) an "effective source" and
(iii) a new residual amplitude correction $(\tilde{\rho}_\lm^H)^{2\ell}$. In
the test-mass limit, we use a frequency-domain perturbative approach to
accurately compute numerically the horizon-absorbed fluxes along a sequence of
stable and unstable circular orbits and we extract from them the functions
$\tilde{\rho}_\lm^H$. These quantities are then fitted via rational functions.
The resulting analytically represented test-mass knowledge is then suitably
{\it hybridized} with lower-order analytical information that is valid for any
mass ratio. This yields a resummed representation of the absorbed flux for a
generic, circularized, nonspinning black-hole binary. Our result adds new
information to the state-of-the-art calculation of the absorbed flux at
fractional 5 post-Newtonian order [S. Taylor and E. Poisson, Phys. Rev. D {\bf
78} 084016 (2008)], that is recovered in the weak-field limit approximation by
construction.
