  The understanding of the fermionic sector of the worldvolume D-brane dynamics
on a general background with fluxes is crucial in several branches of string
theory, like for example the study of nonperturbative effects or the
construction of realistic models living on D-branes. In this paper we derive a
new simple Dirac-like form for the bilinear fermionic action for any Dp-brane
in any supergravity background, which generalizes the usual Dirac action valid
in absence of fluxes. A nonzero world-volume field strength deforms the usual
Dirac operator in the action to a generalized non-canonical one. We show how
the canonical form can be re-established by a redefinition of the world-volume
geometry.
