CONDENSED CONSLOIDATED STATEMENTS OF CHANGES IN STOCKHOLDERS' EQUITY (UNAUDITED) - USD ($) $ in Millions	Total	Ordinary Shares	Capital in Excess of Par Value of Ordinary Shares	Accumulated Deficit	Accumulated Other Comprehensive Income (Loss)	Non-controlling Interest
Beginning balance at Dec. 31, 2021	$ 3,418.4	$ 450.7	$ 9,160.8	$ (4,903.8)	$ (1,305.0)	$ 15.7
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	(45.9)			(59.6)		13.7
Other comprehensive income (loss)	(46.4)				(42.0)	(4.4)
Issuance of ordinary shares, net of shares withheld for tax	(0.1)	1.5	(1.6)
Share-based compensation	19.0		19.0
Other	(0.6)			(0.6)
Ending balance at Jun. 30, 2022	3,344.4	452.2	9,178.2	(4,964.0)	(1,347.0)	25.0
Beginning balance at Mar. 31, 2022	3,490.4	452.2	9,169.1	(4,969.7)	(1,185.3)	24.1
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	7.8			2.1		5.7
Other comprehensive income (loss)	(166.5)				(161.7)	(4.8)
Share-based compensation	9.1		9.1
Other	3.6			3.6		0.0
Ending balance at Jun. 30, 2022	3,344.4	452.2	9,178.2	(4,964.0)	(1,347.0)	25.0
Beginning balance at Dec. 31, 2022	3,276.7	442.2	9,109.7	(5,010.0)	(1,301.7)	36.5
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	(88.5)			(86.8)		(1.7)
Other comprehensive income (loss)	38.3				41.5	(3.2)
Issuance of ordinary shares, net of shares withheld for tax	(17.3)	2.8	(20.1)
Share-based compensation	21.6		21.6
Shares repurchased and cancelled	(100.0)	(6.9)	(93.1)
Other	0.4			0.4
Ending balance at Jun. 30, 2023	3,131.2	438.1	9,018.1	(5,096.4)	(1,260.2)	31.6
Beginning balance at Mar. 31, 2023	3,242.7	441.6	9,056.8	(5,009.5)	(1,288.1)	41.9
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	(96.3)			(87.2)		(9.1)
Other comprehensive income (loss)	26.7				27.9	(1.2)
Issuance of ordinary shares, net of shares withheld for tax	(2.7)	0.1	(2.8)
Share-based compensation	10.5		10.5
Shares repurchased and cancelled	(50.0)	(3.6)	(46.4)
Other	0.3			0.3		0.0
Ending balance at Jun. 30, 2023	$ 3,131.2	$ 438.1	$ 9,018.1	$ (5,096.4)	$ (1,260.2)	$ 31.6