It is said that Adi Shankaracharya installed the Sri Chakra in many temples. Is there a list and description of temples where Adi Shankaracharya installed Sri Chakra?
I was interested in the same question, as I had visited many of them. I did some research. I went through the list of all the temples that have a Sri Yantra, and then figured out which all were established by Sri Shankaracharya. As has already been mentioned, there is no standard list, and many of them are claimed to be installed by Adi Shankaracharya. There are no historical records available. I have tried to keep it as clean as possible in order to remove any spurious places. (I have also added a reference to where I found the quote.) The following are the list of temples:
Kanakadurga, Vijaywada, Andhra Pradesh.
Adi-Sankaracharya visited the temple and installed the Srichakra and initiated workship of Kanaka Durga in vedic ways. - http://www.kanakadurgatemple.org/historyinEnglish.aspx
Sharadamba, Sringeri, Karnataka.
Originally it was an unpretentious shrine with the Murti of Sharada made of sandalwood, installed over the Sri Chakra that Sri Adi Shankara carved on a rock - https://www.sringeri.net/temples/sri-sharadamba
Mahalakshmi, Kolhapur, Maharashtra.
Kamakshi, Kanchi, Tamil Nadu.
Adi Shankaracharya, the famous 8th century CE scholar and saint, re-established the Sri Chakra in this Kamakshi Devi temple in the trough-like structure in that shrine. - https://en.wikipedia.org/wiki/Kamakshi_Amman_Temple
Kamakshi, Nellore, Andhra Pradesh.
It is said that Adi Sankaracharya has installed srichakram in the sanctum sanctorum of Kamakshi shrine. - https://www.flickr.com/photos/vsramachandran/30636243424 *
Kamakshi, Chennai, Tamil Nadu.
The Adi Shankaracharya is believed to have visited Mangadu and installed a Sri Ardhameru Chakram at this place. - http://www.mangadukamakshi.tnhrce.in/history.html
Nimishamba, Mysore, Karnataka.
the priest tells me that they believe that it dates back to the years of Adi Shankaracharya and point to a ‘srichakra’ carved on a stone in front of the deity. - https://www.thehindu.com/features/metroplus/travel/boon-a-minute/article3896841.ece
Meenakshi, Shivanasamudra, Karnataka
Adi Shankaracharya is believed to have consecrated the Shri Chakra to which the standing goddess’ eyes are directed. The idol is life-like in size and appearance - https://www.deccanherald.com/content/589521/of-temples-legends.html
Mookambika, Kollur, Karnataka.
It has been installed in various temples, including the Kamakshi Temple in Kanchipuram and the Mookambika Temple in Kollur (by Sri Adi Shankaracharya). - https://www.deccanherald.com/content/377593/significance-sri-chakra.html
Brahmaramba, Srisailam, Andhra Pradesh
A story preserved in the folklore narrates that, Adisankara, saw the violent form of Bhramaramba ?Devi and to reduce her violent power, installed Srichakra in front of the Garbhagriha - http://www.srisailamonline.com/about-main-temple.html
Kali, Tiruvottiyur, Tamil Nadu
Adi Shankara is said to have installed a chakra to calm down the Devi and to make her Sowmya roopi - https://en.wikipedia.org/wiki/Thyagaraja_Temple,_Tiruvottiyur
There is some mention about the Sri Chakra being installed at the Kamakhya temple in Guwahati, and Durga Parmeshwari temple in Kateel as well, but I did not find much information about it.
There is some mention that the Sri Chakra was installed at Jagadamba Sharika Bhagwati in Kashmir by Adi Shankaracharya, but this document tells, "In fact there is no historical evidence or chronicle of that era that Adi Shankaracharya visited Kashmir during short span of his life.".
It is unlikely that the moulded gold/ brass srichakra that we see in those temples today was installed during adi shankaracharya's time. Wooden idols were used during those times leave alone stone or metal idols or religious insignia. Madhaviya shankara Vijaya does not mention adi Shankaracharya installing srichakras at any of those temples. In sringeri, the temple record does say that a srichakra was carved on the rock which they saw when the wooden idol was replaced by vidyaranya around 12-13 century. So it is likely done by adi Shankaracharya. But no one knows how it looks, whether the design itself has undergone any changes, and the beeja mantras that are carved on some of the Sri Chakras are based on later texts.
Also, of late it has become a fad to attribute any shloka/temple of Devi to adi Shankaracharya just to get publicity.