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The Reds signed the striker on transfer deadline day on a permanent deal from Newcastle United after a £125million fee was agreed between both clubs.Following his move to Liverpool, Isak was called up to the Sweden squad for their round of World Cup qualifiers this month.
The 25-year-old did not feature in the first fixture against Slovenia last week and was an unused substitute.
Isak was named on the bench again for the clash against Kosovo on Monday night, but was given some valuable minutes this time around.
Sweden manager Jon Dahl Tomasson introduced the striker to the match in the 72nd minute, with Isak replacing his former Newcastle teammate, Anthony Elanga.
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Sweden went on to lose the game 2-0, the same scoreline as when Isak was substituted in the contest.
Just 10 minutes into his cameo, the Liverpool striker was given a yellow card by referee Allard Lindhout.
There was late drama in the game as Kosovo had a player sent off in stoppage time.
Lindon Emerllahu was shown two yellow cards in the clash at the Fadil Vokrri Stadium and was given his marching orders despite only being on the pitch for seven minutes after being substituted on in the closing stages.
Isak will now return to Merseyside this week with a view to being awarded his debut for Liverpool at the weekend.
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