In this paper, we study the K0-group of the C?-algebra associated to a
pinwheel tiling. We prove that it is given by the sum of Z + Z^6 with a
cohomological group. The C?-algebra is endowed with a trace that induces a
linear map on its K0-group. We then compute explicitly the image, under this
map, of the summand Z+Z^6, showing that the image of Z is zero and the image of
Z^6 is included in the module of patch frequencies of the pinwheel tiling. We
finally prove that we can apply the measured index theorem due to A.