The humbling scoreline sent Dortmund top of the 36-team Champions League standings, with two wins from two matches and a goal difference of nine, while Celtic plunged from third to 19th.
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Atletico made a strong start with Griezmann opening the scoring in the sixth minute with a low shot from the edge of the box.
Atletico Madrid battled back twice to draw 2-2 at Celtic in a thrilling Champions League Group E clash on Wednesday in which the Spanish side played the last few minutes with 10 men.
The 50-year-old returns to Parkhead just over four years after leaving the Scottish Premiership giants to take charge of Leicester City.
Luka Modric and Rodrygo netted from the spot following two handball decisions before Josip Juranovic saw his effort from 12 yards saved.
The 28-year-old Celtic and Rangers target has been outstanding for Livi since they snapped him up from Queen of the South in 2021 and has been one of the stand-out centre-backs in Scottish football over the last 12 months.
In a barnstorming first-half, Liel Abada fired the home side ahead after eight minutes and the Israel winger grabbed a second just before the break.
The Northern Irishman has signed a deal that will take him up to the end of the 2023-24 campaign.
The Super Eagles – one of the main contenders to lift the trophy – were defeated 1-0 by Tunisia in the last 16 of the competition, courtesy of Youssef Mskani’s goal early in the second half.
The 18-year-old joins from English Premier League side Watford.
The Scottish international, who arrived at the Emirates from Celtic in 2019 in a move worth around £25million, has put pen to paper on a five-year deal to keep him in north London until 2026.
Steven Gerrard has claimed the first major league title of his managerial career, with Rangers now holding an unassailable 20-point lead in the league table.
The attacker had been watched by both sides of the Glasgow divide with pre-contracts being considered by both outfits.
The striker is currently on loan at German Bundesliga side Union Berlin and a number of clubs, including the Hoops, are aware of his availability in the January window.
Gerrard is looking to guide his side to a 19-point lead over their bitter rivals.
The 22-year-old attracted interest from clubs in the summer after an impressive campaign last season and he is now on Celtic’s radar.
But the Italians had to withstand a late barrage from the Scottish champions to secure the three points.
The group stages get underway on October 19, with six rounds of group games running through to mid-December
The 20-year-old Dubliner joined Celtic from Southampton in 2019 but has yet to play a competitive fixture for the Hoops.
The Dens Park side have already completed the signing of Nicholas Hamilton but want to further bolster their attacking options.