Sector giant BHP group BHP.AX and Rio Tinto RIO.AX traded in the negative territory. By Nausheen Thusoo May 10 (Reuters) - Australian shares fell on Tuesday, weighed by weakness in financial and mining stocks, while investors remained cautious ahead of a U.S. consumer price index report scheduled to come later in the day. Investors are eagerly waiting for the U.S. consumer price data that could damage hopes for interest rate cuts later this year if inflation fails to show much of a decline.