We present optical photometry of the GRB 060912A afterglow obtained with ground-based telescopes, from about 100 sec after the GRB trigger till about 0.3 day later, supplemented with the Swift optical afterglow data released in its official website. The optical light curve (LC) displays a smooth single power-law decay throughout the observed epochs, with a power-law index of about -1 and no significant color evolution. This is in contrast to the X-ray LC which has a plateau phase between two normal power-law decays of a respective index of about -1 and -1.2. It is shown by our combined X-ray and optical data analysis that this asynchronous behavior is difficult to be reconciled with the standard afterglow theory and energy injection hypothesis. We also construct an optical-to-X-ray spectral energy distribution at about 700 sec after the GRB trigger. It displays a significant flux depression in the B-band, reminding us of the possibility of a host-galaxy (at z=0.937) 2175-A dust absorption similar to the one that characterizes the Milky Way extinction law. Such an identification, although being tentative, may be confirmed by our detailed analysis using both template extinction laws and the afterglow theory. So far the feature is reported in very few GRB afterglows. Most seem to have a host galaxy either unusually bright for a GRB, just like this one, or of an early type, supporting the general suggestion of an anti-correlation between the feature and star-forming activities.
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