  In this work, we follow the recently revisited f(R) theory of gravity for
studying the interaction between quantum scalar particles and the gravitational
field of a generalized black hole with an f(R) global monopole. This background
has a term playing the role of an effective cosmological constant, which
permits us to call it as Schwarzschild-Anti-de Sitter (SAdS) black hole with an
f(R) global monopole. We examine the separability of the Klein-Gordon equation
with a non-minimal coupling and then we discuss both the massless and massive
cases for a conformal coupling. We investigate some physical phenomena related
to the asymptotic behavior of the radial function, namely, the black hole
radiation, the quasibound states, and the wave eigenfunctions.
