Building façade or building roof having a composite system for fastening natural stone panels or ceramic tiles to an outer side of a supporting substrate, comprising: a first adhesive layer system adheringly applied to an outer side of a supporting substrate; a thermal insulation element adheringly applied to an outer side of the first adhesive layer system; a second adhesive layer system adheringly applied to an outer side of the thermal insulation element, wherein the first adhesive layer system, the thermal insulation element and the second adhesive layer system form a thermal insulation composite system; wherein the second adhesive layer system has at least one embedding adhesive layer and an embedding adhesive layer reinforcing element embedded therein, wherein an inner side of the embedding adhesive layer is adheringly applied to the outer side of the thermal insulation element, and the embedding adhesive layer reinforcing element has an alkali-resistant glass fibre and is formed as a reinforcing fabric, a panel adhesive layer system adheringly applied to an outer side of the second adhesive layer system; and natural stone panels or ceramic tiles adheringly applied to an outer side (56, 74) of the panel adhesive layer system, characterized in that the second adhesive layer system further has a compensating adhesive layer and a compensating adhesive layer reinforcing element embedded therein, wherein an inner side of the compensating adhesive layer is adheringly applied to an outer side of the embedding adhesive layer, and wherein the compensating adhesive layer reinforcing element has an alkali-resistant glass-aramid fibre and is formed as an armour fabric. a first adhesive layer system adheringly applied to an outer side of a supporting substrate; a thermal insulation element adheringly applied to an outer side of the first adhesive layer system; a second adhesive layer system adheringly applied to an outer side of the thermal insulation element, wherein the first adhesive layer system, the thermal insulation element and the second adhesive layer system form a thermal insulation composite system; wherein the second adhesive layer system has at least one embedding adhesive layer and an embedding adhesive layer reinforcing element embedded therein, wherein an inner side of the embedding adhesive layer is adheringly applied to the outer side of the thermal insulation element, and the embedding adhesive layer reinforcing element has an alkali-resistant glass fibre and is formed as a reinforcing fabric, a panel adhesive layer system adheringly applied to an outer side of the second adhesive layer system; and natural stone panels or ceramic tiles adheringly applied to an outer side (56, 74) of the panel adhesive layer system, characterized in that the second adhesive layer system further has a compensating adhesive layer and a compensating adhesive layer reinforcing element embedded therein, wherein an inner side of the compensating adhesive layer is adheringly applied to an outer side of the embedding adhesive layer, and wherein the compensating adhesive layer reinforcing element has an alkali-resistant glass-aramid fibre and is formed as an armour fabric.