I will discuss joint work with Akshay Venkatesh on GL2(Z)-cocycles valued in second K-groups of the function fields of the squares of the multiplicative group over the rationals and of a universal elliptic curve over a modular curve, as well as their specializations to explicit, Hecke-equivariant maps taking modular symbols to special elements in second motivic cohomology groups of cyclotomic fields and modular curves. With an eye towards generalizations, I hope to explain the point of view by which these group cohomology classes are viewed as arising from classes in equivariant motivic cohomology.