The retired number 4 jersey was hung up in the rafters above the playing court of the Nikos Galis Olympic Indoor Hall, along with the club's trophy banners.

His potential was proven to be great in the 1991 FIBA Europe Under-16 Championship, where Alvertis led the Greek team to the silver medal alongside Panagiotis Liadelis.

Consequently, young Alvertis had to wait until the 1993–94 season to get significant playing time on a team with high ambitions, as PAO reached the EuroLeague Final Four.

[8] Alvertis averaged 13 points per game, forcing Head Coach Božidar Maljković to state that he already was to be counted as one of the very best players in Europe.

Using his sharp shooting with a rare maturity for a player his age, he was a major contributor to his team's march towards a second consecutive EuroLeague Final Four.

[11] In the Greek League semifinals, Panathinaikos faced a Panionios team under Dušan Ivković, featuring the likes of Žarko Paspalj and Fanis Christodoulou.

Alvertis cemented his role as one of Panathinaikos' main stars, in spite of the fact that the team experienced a dispiriting 1996–97 season.

Although he increased his scoring average to 12.7 points per game, he was unable to help PAO reach the 1997 EuroLeague Final Four as they were bested by eventual champions Olympiacos in the quarterfinal playoffs.

[12] The Greek League outcome would add up to the season's drama, as Alvertis' 29 points against PAOK in Game 2 of the quarterfinal playoffs were not enough to prevent a 90–85 defeat.

Strengthened by the addition of another NBA legend in Byron Scott for the 1997–98 season, Panathinaikos won their first national league title since 1984.

[13] In the memorable semifinal playoff series, AEK was coming off of a 1998 Euroleague Finals campaign, led by the likes of Bane Prelević, Willie Anderson and Victor Alexander.

Following the win in the final series against PAOK and Peja Stojaković, he was voted to the All-Greek League Team, alongside teammate Dino Radja.

After an unexpected failure to reach the EuroLeague Top 8 in the 1998–99 season, Alvertis won one more Greek League title.

Panathinaikos beat Olympiacos in the finals, after breaking home court advantage and winning the decisive Game 5 in the Peace and Friendship Stadium.

[14] As for the Greek League, Olympiacos had once again a very solid team that year, featuring Dino Radja, David Rivers and Nikos Oikonomou.

[17] Prior to that, he had led the Greens to their first Greek Cup since 1996, scoring 22 points in the final against Aris, and being named the tournament's MVP.

[20] Along with the team's new stars Dimitris Diamantidis, Jaka Lakovič, and Mike Batiste, PAO made it to the 2005 EuroLeague Final Four in Moscow, where they lost to Šarūnas Jasikevičius' and Anthony Parker's Maccabi Tel Aviv.

In their playoff series, TAU Ceramica pulled off an upset during the decisive third game in Athens, thus preventing PAO from reaching the 2006 EuroLeague Final Four.

On April 12, 2022, Fragkiskos Alvertis was removed from his administrative positions and replaced with Argyris Pedoulakis, after a rather unfortunate season in EuroLeague.

[22] The following year, Alvertis was already a permanent member of the Greek team and took part at the 1996 Summer Olympic Games in Atlanta, Georgia.

At the EuroBasket 1997, Greece once again started the tournament with very high ambitions, and a victory against title contender Russia, in the qualifying group raised their hopes even higher.

Alvertis averaged 13.2 points and a surprisingly high 6.2 rebounds per game, being a major contributor to Greece's fourth-place finish at the tournament.

[25] He most notably scored the three-pointer that sealed the fate of the quarterfinals match against Spain, giving Greece a 65–58 advantage with 53 seconds left in the game.

After leading the team in offense, with an average of 18.1 points per game in the qualifying round, everything seemed to indicate a great upcoming EuroBasket for the Greek star.

Without its offensive leader, and without key players Nikos Oikonomou and Efthimios Rentzias, who were also injured, Greece finished in an embarrassing sixteenth and last place at the tournament.

Alvertis, coming off a great club year with Panathinaikos, and Giorgos Sigalas, had to show to the younger generation of Greek players the road to success.

Consequently, in order to reach the quarterfinals, Greece's game against rising power Germany appeared to be a difficult task.

[4] While his relative lack of athleticism and average all around skills did not allow him to create his own shot on a consistent basis, his exceptional shooting prowess, with a rare combination of height and mechanics, turned him into a very hard to defend mismatch on the perimeter.

[29] Over the last five years of his career, he mainly played at the power forward position, due to his height and size, thus adjusting to the increased pace of the game in the new millennium.

Panathinaikos's Head Coach Željko Obradović once said, "Alvertis is the best captain I ever had", paying tribute to the team leadership skills of his star.