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Trump, who takes office on Jan. 20, is scheduled to hold a news conference on Wednesday that will be his first since winning the election in November.
The Nikkei dropped 0.8 percent to 19,301.44. The broader Topix was down 0.7 percent at 1,542.31 and the JPX-Nikkei Index 400 fell 0.8 percent to 13,816.61.