An endomorphism algebra realization problem and Kronecker embeddings for algebras of infinite representation type

Let R be a finite-dimensional algebra over an algebraically closed field K. One of the main aims of this paper is to prove that if the algebra R is loop-finite or R is strongly simply connected then the following three conditions are equivalent: (a) the algebra R is of infinite representation type, (b) the category mod(R) of finitely generated right R-modules contains a full and exact subcategory equivalent with the category of Kronecker modules, (c) every K-algebra A is isomorphic to a K-algebra of the form EndR(X), where X is a right R-module.