  This paper is motivated by the introduction of a new functional setting of
General Relativity (GR) based on the adoption of suitable group non-local point
transformations (NLPT). Unlike the customary local point transformatyion
usually utilized in GR, these transformations map in each other intrinsically
different curved space-times. In this paper the problem is posed of determining
the tensor transformation laws holding for the $4-$% acceleration with respect
to the group of general NLPT. Basic physical implications are considered. These
concern in particular the identification of NLPT-acceleration effects, namely
the relationship established via general NLPT between the $4-$accelerations
existing in different curved-space times. As a further application the tensor
character of the EM Faraday tensor.with respect to the NLPT-group is
established.
