An algebra group is a group of the form G = 1+J where J = J(A) is the Jacobson radical of a finite-dimensional associative algebra A (with identity). A Theorem of Z. Halasi asserts that, in the case where A is defined over a finite field F, every irreducible complex representation of G is induced by a linear representation of a subgroup of the form H = 1+J(B) for some subalgebra B of A. In this talk, we assume that F has odd characteristic p and (A,s) is an algebra with involution. Then, s naturally defines a group automorphism of G = 1+J, and thus we may consider the fixed point subgroup G(s). In this situation, we may use Glauberman's correspondence to show that every irreducible complex representation of G(s) is induced by a linear representation of a subgroup of the form H(s) where H = 1+J(B) for some s-invariant subalgebra B of A. A particular situation occurs for Sylow p-subgroups of the classical groups of Lie type (defined over F). If time permits, we will also introduce the notion of a supercharacter and discuss some applications to Combinatorics.