"Bernie is the heartbeat of the team," Lineen said. "He's been here for a few years now and has a great attitude and work ethic. The guy is exceptional. He looks after himself really well and takes real pride in his performance.
"He wants to do well for Glasgow and I think he's really developed his game over the last three years, so much so that he got back into the Argentina team. But now it's all about Glasgow and it's great to have him around."
Stortoni added: "I'm so happy to be staying in Glasgow. Over the last three years the team has been building and we're still working very hard. That's important to me because my main thing when I play rugby is to give everything.
"I'm very proud to live and play in Glasgow. I have very strong feelings for this club because I believe it's the best place I've ever played professional rugby. Glasgow is now my home away from home."
In addition to Stortoni's commitment, centre/wing Dave McCall, recruited from Heriot's, has impressed Lineen so much during the time he has been on a temporary contract to merit a fulltime position for a further two years.
Lineen continued: "There's a lot of potential there with Dave, he's an exciting young talent. There are areas of his game that he still needs to work on but he's got pace, he's tough and we just need to fine tune a few things with him.
"I'm delighted to have a guy like him because he's a real threat, and again, he's a guy who works hard."
Finally, Heriot's and National Academy flanker Chris Fusaro, a product of the prolific Howe of Fife/Bell Baxter High School youth set-up, has been handed a two-year professional contract having made his first start for the Warriors against Cardiff Blues almost two weeks ago.
Lineen said of the youngster: "You look at the guy and speak to him and you know there is a real burning desire. There's a real intensity to his game.
"The Cardiff game was a bit of an eye-opener for him but he didn't shirk. He put the tackles in, he worked really hard and I know he'll get better. He's a young lad, he's really committed and he's really keen."
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