The Algerian had been a target for Man City on the final day of the January transfer window.
His first came from some neat play down the left, which led to a precision cross into the six-yard box from where Aguero made no mistake.
It did not take the home side long to establish an advantage, Sterling tapping in from close range following an exquisite De Bruyne cross between Schmeichel and his defenders.
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The other 32, including three-time Games gold medallist An, were also left off the list of Russians invited to Pyeongchang . Stephen Hess, an worldwide sports lawyer based in Colorado Springs, Colorado, said the decision was a victory for the IOC.
Argentine striker Aguero netted all his goals in a devastating second-half showing - twice finishing from Kevin de Bruyne's flawless passes, punishing a Kasper Schmeichel error by chipping into the net and curling in a sublime fourth.
Mahrez's sudden U-turn could see Puel provide him with the flawless platform with which to show City why they should maintain their interest when the transfer window reopens in the summer.
The Argentine converted De Bruyne's teasing cross in the 48th minute and collected another pass from the Belgian to fire through Kasper Schmeichel's attempted save.
After controlling the first 20 minutes, City were suddenly rocked as the visitors hit back out of nowhere.
Many pundits, including Neville and former England captain Alan Shearer, interpreted Guardiola's decision as a protest against a number of risky challenges made on City players during recent matches.
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Medicare: Repeal the Independent Payment Advisory Board (IPAB), a Medicare cost-cutting group created by the Affordable Care Act. That was a turnaround from Tuesday, when Mr Trump had said he would "love" a shutdown if he did not get his way on immigration .
Pep Guardiola has insisted Manchester City are not to blame for Riyad Mahrez's absence from Leicester City training. They play more, they play between channels and have more passes.
But after the break they were transformed as Sergio Aguero and Kevin De Bruyne put on an attacking masterclass to help the runaway leaders rout the 2016 champions 5-1. The pace of Vardy was being utilised less in the second half, perhaps due to a change in the nature of City's defending, but even on the counter they didn't look quite as threatening as they had done.
And a Nicolas Otamendi error 24 minutes in was punished in ruthless fashion by Jamie Vardy, reminding City there is more to Leicester than just Mahrez - who was eventually introduced in the 62nd minute. It was a brilliant way to grab his third goal, and finished off Leicester completely in emphatic style.
Mahrez has been unavailable for Leicester's last two Premier League matches, but the winger says he was not AWOL as had been widely reported.
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Schalke refused to buckle, however, and was rewarded for its intensity when Franco di Santo equalized before the half-hour mark. Eintracht Frankfurt defeated bottom club Cologne 4-2 at home to move to fourth, the last place for a Champions League playoff.