  A study on the relation between the smooth structure of a symplectic homotopy
K3 surface and its symplectic symmetries is initiated. A measurement of
exoticness of a symplectic homotopy K3 surface is introduced, and the influence
of an effective action of a K3 group via symplectic symmetries is investigated.
It is shown that an effective action by various maximal symplectic K3 groups
forces the corresponding homotopy K3 surface to be minimally exotic with
respect to our measure. (However, the standard K3 is the only known example of
such minimally exotic homotopy K3 surfaces.) The possible structure of a finite
group of symplectic symmetries of a minimally exotic homotopy K3 surface is
determined and future research directions are indicated.
