Here we go again. Just a week after the Blackstone Group began trading (its shares are down 4.1 percent from the offering price), private equity firm Kohlberg Kravis Roberts & Co. has decided to move forward with an initial public offering. KKR's IPO, which has been in the works for several weeks, is bound to raise new questions about whether the private equity boom is peaking (actually KKR has been relatively active in the last few weeks). It also fuels the longstanding rivalry between Blackstone's Steve Schwarzman and KKR chief Henry Kravis. KKR said in a filing this afternoon that it wants to raise $1.25 billion. It expects to complete the proposed offering during the third or fourth quarter. (Deal Book)