We consider a two-dimensional periodic reactive Lorentz gas, in which a mov
ing point particle undergoes elastic collisions on fixed hard disks and ann
ihilates on absorbing disks, called sinks. We present clear evidence of the
existence of a fractal repeller in this open system. Moreover, we establis
h a relation between the reaction rate, describing the macroscopic evolutio
n of the system, and two characteristic quantities of the microscopic chaos
: the average Lyapunov exponent and the Hausdorff codimension of the fracta
l repeller.