Income taxes - Narratives (Details) € in Billions	12 Months Ended
	Dec. 28, 2019 USD ($)	Jan. 02, 2021 USD ($)	Dec. 28, 2019 EUR (€)	Dec. 29, 2018 USD ($)
Operating Loss Carryforwards
Operating loss carryforwards, not subject to expiration		$ 3,543,100,000
Operating loss carryforwards, subject to expiration		2,785,300,000
Operating loss carryforward net of valuation allowance		654,700,000
Operating loss carryforwards, valuation allowance		885,900,000
Deferred tax asset, net	$ 821,000,000.0	902,800,000
Interest expense carryforward		515,500,000
Deferred tax interest expense net of valuation allowance		86,500,000
Deferred tax asset, interest expense valuation allowance		35,600,000
Deferred tax asset, valuation allowance	1,200,200,000	1,219,900,000
Taxable temporary differences related to investments in subsidiaries		1,707,000,000.0
Deferred tax liability related to subsidiaries	40,900,000	40,600,000
Disallowed interest carryforward		26,000,000
Unrecognized tax benefit that if recognized would impact tax rate		94,600,000
Accrued taxes interest and penalties	19,600,000	12,300,000		$ 13,400,000
Anticipated decrease in income tax liability from settlement of tax audit		3,300,000
United Kingdom, Luxembourg, Belgium
Operating Loss Carryforwards
Deferred tax asset, net		29,500,000
Luxembourg, the United Kingdom and United States
Operating Loss Carryforwards
Deferred tax asset, net	586,200,000
Capital loss carryforward
Operating Loss Carryforwards
Tax credit carryforward		799,500,000
Deferred tax asset, net		0
Tax credit carryforward, valuation allowance		151,900,000
Foreign tax credit carryforward
Operating Loss Carryforwards
Tax credit carryforward		143,400,000
Deferred tax asset, net		2,500,000
Tax credit carryforward, valuation allowance		140,900,000
Other tax credits
Operating Loss Carryforwards
Tax credit carryforward		4,500,000
Deferred tax asset, net		3,400,000
Tax credit carryforward, not subject to expiration		500,000
Tax credit carryforward, subject to expiration		4,000,000.0
Deferred tax asset, valuation allowance		1,100,000
Net Operating Loss
Operating Loss Carryforwards
Indefinite lived net operating loss | €			€ 2.1
Luxembourg
Operating Loss Carryforwards
Change in valuation allowance	608,600,000
Deferred tax asset, net	579,000,000.0
Domestic And Foreign Authorities
Operating Loss Carryforwards
Operating loss carry forward		6,152,100,000
State and Local Jurisdiction
Operating Loss Carryforwards
Operating loss carry forward		176,300,000
Czech Republic
Operating Loss Carryforwards
Expiration of manufacturing incentives	5,000,000.0
Manufacturing incentives utilized	$ 4,100,000
India | Minimum
Operating Loss Carryforwards
Reasonable decrease in unrecognized tax benefit in the next 12 months		1,000,000
India | Maximum
Operating Loss Carryforwards
Reasonable decrease in unrecognized tax benefit in the next 12 months		$ 2,000,000