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)	(50.5)			(69.9)		19.4
Other comprehensive income (loss)	(171.6)				(164.4)	(7.2)
Issuance of ordinary shares, net of shares withheld for tax	(0.1)	1.5	(1.6)
Share-based compensation	28.9		28.9
Shares repurchased and cancelled	(50.1)	(5.8)	(44.3)
Other	(0.7)			(0.2)		(0.5)
Ending balance at Sep. 30, 2022	3,174.3	446.4	9,143.8	(4,973.9)	(1,469.4)	27.4
Beginning balance at Jun. 30, 2022	3,344.4	452.2	9,178.2	(4,964.0)	(1,347.0)	25.0
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	(4.6)			(10.3)		5.7
Other comprehensive income (loss)	(125.2)				(122.4)	(2.8)
Share-based compensation	9.9		9.9
Shares repurchased and cancelled	(50.1)	(5.8)	(44.3)
Other	(0.1)			0.4		(0.5)
Ending balance at Sep. 30, 2022	3,174.3	446.4	9,143.8	(4,973.9)	(1,469.4)	27.4
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)	5.2			3.2		2.0
Other comprehensive income (loss)	(16.2)				(20.0)	3.8
Issuance of ordinary shares, net of shares withheld for tax	(17.1)	2.9	(20.0)
Share-based compensation	30.7		30.7
Shares repurchased and cancelled	(150.1)	(9.6)	(140.5)
Dividends declared and paid	(21.8)			(21.8)
Other	2.6			3.1		(0.5)
Ending balance at Sep. 30, 2023	3,110.0	435.5	8,979.9	(5,025.5)	(1,321.7)	41.8
Beginning balance at Jun. 30, 2023	3,131.2	438.1	9,018.1	(5,096.4)	(1,260.2)	31.6
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Net income (loss)	93.7			90.0		3.7
Other comprehensive income (loss)	(54.5)				(61.5)	7.0
Issuance of ordinary shares, net of shares withheld for tax	0.2	0.1	0.1
Share-based compensation	9.1		9.1
Shares repurchased and cancelled	(50.1)	(2.7)	(47.4)
Dividends declared and paid	(21.8)			(21.8)
Other	2.2			2.7		(0.5)
Ending balance at Sep. 30, 2023	$ 3,110.0	$ 435.5	$ 8,979.9	$ (5,025.5)	$ (1,321.7)	$ 41.8